Page 1 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
CCM6/CCM6+ Unit 13 Collect, Analyze, and Display Data 2016 – 2017 Name: ____________________________________ Math Teacher: _____________________________ Projected Quiz Date: __________________________ Projected Test Date: __________________________ Main Idea
Page(s)
Unit 13 Vocabulary
2-3
Statistical Questions
4-5
Find and Compare Statistical Measures
6-9
More with Mean, Median, Mode, Range
10 - 18
Histograms
19 - 27
Mean and Measures of Center
28 - 30
Box Plots
31 - 35
Mean Absolute Deviation (MAD)
36 - 38
MAD and IQR as Measures of Variability
39 - 49
More Practice with Histograms and Box Plots
50 - 56
Unit 13 Study Guide
57 - 59
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Page 2 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
CCM6/CCM6+ Unit 13: Collect, Analyze, Display Data Vocabulary Statistics
The practice of collecting and analyzing data in large quantities
Data
Values such as counts, ratings, measurements, or opinions that are gathered to answer questions.
Mean
A value that represents the "evening out" of the values in a set of data
Median
The number that is the midpoint of a set of data
Mode
The data value that occurs the most
Range
The difference between the least value and the greatest value in a data set
Line Plot
A quick, simple way to organize data along a number line where the X's (or other symbols) above a number represent how often each value is mentioned
Measures of Center
Establish a central location in the data set
Measures of Variability
Establish the degree of variability (or scatter) of the individual data values and their deviations from the measures of center
Histogram
A display that shows the distribution of numeric data. The range of data values, divided into intervals, is displayed on the horizontal axis. The vertical axis shows frequency.
Frequency Table
A list of items or intervals that shows the number of times, or frequency, with which they occur.
Interval
is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set
Distribution
The arrangement of values in a data set
Gap
a break or opening
Cluster
a group of things or persons close together
Peak
being at the point of maximum frequency, intensity, use, etc.
Box Plot
a method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data
Quartiles
one of the values of a variable that divides the distribution of the variable into four groups having equal frequencies
Lower Quartile
for a data set with median m, the first quartile is the median of the data values less than m Example: for the data set {1, 3, 6, 7, 10, 12, 14, 15, 22,120}, the first quartile is 6. for a data set with median m, the third quartile is the median of the data values greater than m
Upper Quartile
Example: for the data set {2, 3, 6, 7, 10, 12, 14,15, 22, 120}, the third quartile is 15.
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Page 3 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Outlier
a value that lies far from the "center" of a distribution
Inter-Quartile Range
a measure of variation in a set of numerical data, the inter-quartile range is the distance between the first and third quartiles of the data set Example:for the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15–6= 9.
Five-Number Summary
The minimum value, lower quartile, median, upper quartile, and maximum value
Minimum Value
The lowest value in a data set
Maximum Value
The greatest value in a data set
Mean Absolute Deviation (M.A.D.)
The average distance of all data values from the mean of the set
Variability
Degree to which data are spread out around a center value
Skewed
asymmetry in a frequency distribution
Summary statistics
include quantitative measures of center (median and median) and variability (interquartile range and mean absolute deviation) including extreme values (minimum and maximum), mean, median, mode, range, and quartiles
Symmetrical
characterized by or exhibiting symmetry; well-proportioned, as a body or whole; regular in form or arrangement of corresponding parts
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Page 4 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Intro to Statistics What is Statistics? ________________________________________________________________________________ ________________________________________________________________________________ Why is it important? ________________________________________________________________________________ What are statistical questions? ________________________________________________________________________________ ________________________________________________________________________________ The teacher will show you a variety of questions. Determine whether the question is statistical or non-statistical and write the questions under the correct heading. Statistical
Non-Statistical
Chose one of the statistical questions from the list above and determine how you might find the answer to this question.
What are ways in which you can collect data? 1. 2. 3. 4. 5. 6.
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Page 5 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
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Page 6 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
The mean, the median, the mode, and the range are measures that describe a set of data. This picture will help you learn about each measure. MEAN (average)
MEDIAN (middle)
Add all the values, then divide by the total number of values.
The middle value, when the values are arranged in order.
Measures that
MODE (most)
RANGE
Describe a Set of Data
The value that occurs most often
The difference between the
in a set of data. There can be one mode,
greatest number and the
more than one mode, or no mode.
least number in a set of data.
Tim’s bowling scores for the past 5 games are listed below: 89 98 110 98 105 Write mean, median, mode, or range to answer the following questions about Tim’s scores. 1. The number 98 indicates which measure?
___________________________
2. Tim added up all his scores and divided by 5. Which measure did he find?________________ 3. Tim found that the difference between his highest and lowest score was 21 points. That measure is called the ______________________ 4. Tim noticed that he got a score of 98 twice. Which measure is Tim focusing on? ___________
Terry’s test scores for the past 5 assessments are listed below. Calculate the range, mean, median, and mode. Terry’s Test Scores 76
Range: ___________
Mean: _________
81
94
81
Median: _____________
6
78
Mode: ___________
Page 7 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
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Page 8 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
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Page 9 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
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Page 10 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Finding Statistical Measures and Comparing them to Understand Data
BIG IDEAS….
Shape of a set of data o Symmetrical data…mean and median are close to the same o Skewed data…leans left or right…mean and median are different…mean is pulled left or right
Outliers o When there is an outlier, it pulls the mean up or down o Outliers barely affect the median o If there is an outlier, the median will be more typical for that set of data than the mean
Names: Maxi Swanson
Thomas Petes
Michelle Hughes
Shoshana White
(11)
(11)
(14)
(13)
Deborah Black
Tonya Stewart
Tony Tung
Richard Mudd
(12)
(12)
(8)
(11)
Janice Wong
Bobby King
Charlene Greene
(10)
(9)
(14)
What part of the data above is most important? Create a dot plot (line plot) of the data.
Can you make any conclusions about this data? ________________________________________ Describe the SHAPE of the data…
Symmetrical?
Skewed?
Random?
Write a statistical question about the data above. _________________________________________
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Page 11 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Investigating Statistics…What numbers affect the MEDIAN? 1.
Using the names provided, place them in order from least to greatest. What is the middle number? How many numbers are to the left of the middle number? How many numbers are to the right of the middle number? Middle Number:
______
# of numbers to the left:
______
# of numbers to the right:
______
2. The median is the number that is the midpoint of a set of data. The same number of data values occur before and after the median. What is the median for these data?
3. Remove two names from your data set so that: The median stays the same: _______ when you remove ___________________________ The median increases:
_______ when you remove ____________________________
The median decreases:
_______ when you remove ____________________________
4. Maxi Swanson is moving. When she leaves, what will be the new median for the data set?
5. What would happen to the median of the data set if you add a name with 16 letters?
6.
What would happen to the median of the data set if you add a name with 89 letters?
**What do you call a data point far away from all others? ____________________________
7.
What would be the length of two names that you could add to the data set so that The median stays the same: The median increases: The median decreases:
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Page 12 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Investigating Statistics…What numbers affect the MEAN? Susan has six pets. She made the line plot to show the lengths of her pets’ names. Describe the SHAPE of the data.
What is the mean of the data above?
If you add a 1 letter pet name, what will be the new mean? What will be the new median? How did a low data value change the mean? How did a low data value change the median?
If you remove the 1 and replace it with a 25, what will be the new mean? What will be the new median? How did a high data value change the mean? How did a high data value change the median?
Do very high or very low data values far away from the other data (outliers) change the mean or median more?
When there is an outlier, which measure of center would be better to use for that set of data?
When there is no outlier, which measure of center would be better to use for that set of data?
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Page 13 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Investigating Statistics:How does the SHAPE of the data affect the center? PEAK … CLUSTER … SKEWED … SYMMETRICAL … GAP Describe the shape of the data in the line plot to the right. Mean = ______________ Median = _____________ Mode = ____________ Range = ____________ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Describe the shape of the data in the line plot to the right. Mean = ______________ Median = _____________ Mode = ____________ Range = ____________ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Describe the shape of the data in the line plot to the right. Mean = ______________ Median = _____________ Mode = ____________ Range = ____________ Describe the shape of the data in the line plot to the right. Mean = _________ Median = _________ Mode = __________ Range = ________
Which measures are affected most by the outlier? ___________________________________ 13
Page 14 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
PRACTICE 1. Jessica’s History Test Scores 81 97 99 89
91
50
Range: ________________________________________ Mean: _________________________________________ Median: ________________________________________ Mode: _________________________________________ Which measure of center is best for Jessica—mean or median? Explain.
2. On an exam, three students scored 75, four students scored 82, three students scored 88, four students scored 93, and one student scored 99. If the answer is 88, what is the question? Hint: Write the scores out!
3. Find the mean, median, mode, and range of the dot plot.
Mean: ___________ Median: ___________ Mode: ___________ Range: __________
For the line plot, is mean or median a better measure of center? Explain.
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Page 15 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
The two graphs below show students’ name lengths in two classes.
Ms. Campo’s class:
Mean = _____
7 Median = _____
6 5
Mode = _____
4 3
Range = _____
2 1 0 9 10 11 12 13 14 15 16 17 18 19
Mean = _____
Mr. Young’s class: Median = _____
X
X X X X X X X X X
8
9 10 11 12 13 14 15 16 17 18 19 20
X X X
X
X
X
Mode = _____
Range = _____
1. What is the typical name length for: a) Ms. Campo’s class.
b) Mr. Young’s class.
2. Find the mean, median, mode, and range for both classes in the boxes above. 3. How does the data distribution (SHAPE) compare between these two classes?
3. Since Mr. Young’s class data has an outlier, which measure best represents his data?
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Page 16 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017 1. The
line plot below represents the number of letters written to overseas pen pals by the students at Waverly Middle School. Each "x" represents 10 students. How many students wrote 18 or more letters?
A) 250
B) 8
C) 30
D) 80
2. The
line plot below represents the number of letters written to overseas pen pals by the students at Waverly Middle School. Each "x" represents 10 students. How many students wrote more than 6 and fewer than 12 letters?
A) 110 3. Thirteen
B) 120
C) 100
D) 90
bowlers were asked what their score was on their last game. The scores are shown
below. 183, 152, 155, 181, 176, 193, 171, 170, 186, 170, 187, 159, 183 Find the range of the bowlers' scores. A) 20
B) 41
C) 53
D) 31
4. A
group of friends tested themselves to see how many times each person could hit a tennis ball against the wall without missing. The results are below: 7
15
28
8
21
30
30
10
22
4
17
7
17
22
10
8
Find the range of the data set. A) 26
B) 16
C) 36
D) 23
5. Thirteen
bowlers were asked what their score was on their last game. The scores are shown below. 190, 150, 154, 194, 182, 190, 170, 151, 190, 170, 178, 161, 180 Find the range of the bowlers' scores. A) 56 B) 44 C) 34 D) 23
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Page 17 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017 6. The
line plot below represents the number of letters written to overseas pen pals by the students at Waverly Middle School. Each "x" represents 10 students. How many students wrote 14 or more letters?
A) 140
B) 160
C) 0
D) 14
7. The
line plot below represents the number of letters written to overseas pen pals by the students at Waverly Middle School. Each "x" represents 10 students. How many students wrote more than 6 and fewer than 20 letters?
A) 250
B) 240
C) 230
D) 220
8. A
group of friends tested themselves to see how many times each person could hit a tennis ball against the wall without missing. The results are below: 8
13
22
8
18
28
28
12
25
6
15
8
15
25
12
8
Find the range of the data set. A) 19
B) 22
C) 32
D) 12
9. A
group of friends tested themselves to see how many times each person could hit a tennis ball against the wall without missing. The results are below: 7
11
25
7
25
23
23
15
21
7
12
7
12
21
15
7
Find the range of the data set. A) 28
B) 8
C) 18
D) 15
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Page 18 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
10. Thirteen
bowlers were asked what their score was on their last game. The scores are shown
below. 192, 158, 154, 195, 180, 183, 188, 151, 180, 185, 184, 166, 184 Find the range of the bowlers' scores. A) 56
11.
B) 34
C) 23
D) 44
Which measure is affected MOST by an outlier? A) mean
B) median
C) mode
Why? ________________________________________________________________
12.
Which measure is affected LEAST by an outlier? A) mean
B) median
C) mode
Why? _________________________________________________________________
13. How is a bar graph like a line plot (dot plot)?
14. What kind of data is best for the mode? the median? the mean?
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Page 19 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Histograms
Histogram: ____________________________________________________________________ ____________________________________________________________________ Constructing a Histogram Mrs. Pittman gave her class a history test. The class of 16 students had the following scores:
75, 80, 65, 80, 95, 85, 65, 80, 90, 80, 70, 85, 90, 70, 85, 70
Construct a histogram to represent this data.
Frequency Chart Interval
Tally
Frequency
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Page 20 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
1.
Listed below are the daily high temperatures (◦F) for the first 20 days of April. Choose appropriate intervals to group the data, make a frequency table for the data, and construct a histogram for the data. 55 65
62 60
68 58
75 75
69 80
Frequency Chart Interval
Tally
Frequency
20
78 82
82 74
79 78
85 78
88 72
Page 21 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
2. Thirty people in Max’s neighborhood participated in a Walk-A-Thon fundraiser. The ages of the walkers were as follows: 12 8 32 35 15 47 9 11 16 45 44 19 62 60 a. Make a histogram for the set of data.
15 8
52 23
55 27
70 10
18 34
36 74
29 13
12 59
Frequency Chart Interval
Tally
Frequency
b. Determine the mean and median for this data set.
c. Explain how the median for this data relates to the graph of the data.
d. If the seven youngest participants did not walk and seven members of the Golden Oldies Club (over 70 years of age) took their place, how would this change the graph of the data? Determine the mean and median for this new data set.
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Page 22 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
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Page 23 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
More Practice with Histograms MIGRAINES: HISTOGRAMS Below are data collected from patients who suffer from migraine headaches. The patients were instructed to take their assigned drugs as soon as their headaches began and to record how much time passed before the drugs gave relief. Drug A is a traditional drug, and Drug B is an experimental drug. Each value is the number of minutes (rounded to the nearest two minutes) that elapsed before a patient got relief. Drug A (100 patients)
16, 18, 18, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 32, 32, 34, 36, 38, 38, 40, 42, 44, 44, 46, 46, 48, 50, 54, 56, 56, 58, 58, 62, 62, 64, 64, 66, 68, 68, 70, 70, 70, 72, 72, 74, 76, 76, 76, 78, 78, 80, 80, 80, 82, 82, 84, 84, 86, 88, 88, 88, 88, 90, 90, 90, 90, 90, 92, 92, 92, 92, 94, 94, 94, 96, 96, 98, 98, 98, 98, 100, 100, 100, 102, 102, 102, 104, 104, 106, 106, 108, 108, 108, 110, 110, 112, 114, 118, 120 Drug B (50 patients)
18, 20, 20, 22, 24, 24, 24, 26, 26, 30, 30, 30, 34, 34, 34, 36, 36, 36, 38, 38, 40, 40, 44, 44, 46, 50, 52, 52, 56, 56, 58, 62, 62, 66, 74, 74, 78, 88, 94, 98, 98, 100, 104, 106, 110, 116, 120, 120, 121, 121
1. From examining these data, which drug do you think gave faster relief from headache pain?____ Explain______________________________________________________________________ On the next page you will create a frequency table for each drug. Draw dividing lines in the data above (for each drug) to separate into these intervals:
10-19, 20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80-89, 90-99, 100-109, 110-119, 120-129 Then, fill out the frequency table on the next page according to the amount per interval.
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Page 24 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
More Practice with Histograms
Migraines: Histograms Time to Effect of Drug A (100 patients) Time (minutes)
Frequency
Time to Effect of Drug B (50 patients)
Percentage of Total (100)
Time (minutes)
10 - 19
10 - 19
20 – 29
20 – 29
30 – 39
30 – 39
40 – 49
40 – 49
50 – 59
50 – 59
60 – 69
60 – 69
70 – 79
70 – 79
80 – 89
80 – 89
90 – 99
90 – 99
100 – 109
100 – 109
110 – 119
110 – 119
120 – 129
120 – 129
**To calculate the percent:
# in the interval # 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠 𝑓𝑜𝑟 𝑡ℎ𝑎𝑡 𝑑𝑟𝑢𝑔
24
Frequency
Percentage of Total (50)
• 100 = ______%
Page 25 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
2. Construct a histogram for each data set on the axes provided below. Title your display. Drug A
#
20
of
18
P A T I E N T S
16 14 12 10 8 6 4 2
#
0 Drug B 20
of
18
P A T I E N T S
16
10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
100-109 110-119 120-129
14 12 10 8 6 4 2 0 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
25
100-109 110-119 120-129
Page 26 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
3. From examining the histograms, which drug do you think gave the most relief from headache pain? ________________ Explain._________________________________ ___________________________________________________________________ ___________________________________________________________________ 4. A relative-frequency histogram uses the % in each interval rather than the frequency. Why is this useful for our data sets? What is the advantage of a relative-frequency histogram for our data sets?
Construct two relative-frequency histograms below (one for each Drug). Drug A %
25
of
20
P A T I E N T S
15 10 5 0 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
100-109 110-119 120-129
Time in Minutes To Effect
Drug B %
25
of
20
P A T I E N T S
15 10 5 0 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99
26
100-109 110-119 120-129
Page 27 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Time in Minutes To Effect 5. On the basis of your examination of the relative-frequency histograms, which drug do you think gave faster relief from headache pain? _____________ Explain.
6. Some students get different answers for questions 3 on the previous page and 5 on this page. Why do you think that happens?
7. How does changing the display (frequency histogram or relative-frequency histogram) change the information you can read from the graph?
8. What advantage does the histogram have over the relative-frequency histogram?
9. What advantage does the relative-frequency histogram have over the histogram?
10. What have you learned from this activity?
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Page 28 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
A group of students made the table below. Household Size NAME
# of People
Reggie
6
Tara
4
Brendan
3
Felix
4
Hector
3
Tonisha
4
A. Make stacks of cubes to show the size of each household. 1. How many people are in the six households altogether? Explain
2. What is the mean number of people per household? Explain.
3. How does the mean here compare to the mean for the data on p. 30?
B. What are other ways to determine the mean of a set of data other than using cubes?
C. Make a set of 6 data values that have a mean of 8.
D. Make a set of 5 data values that have a median of 8.
E. Make a set of 5 data with a range of 6, a mean of 6, and a median of 6.
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Page 29 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
For questions 1 and 2, use the line plot below. Number of Children in a Household
0
1
2
3
4
5
6
7
8
9
10
11
12
1. a. What is the median number of children for the 16 households? Explain how to find the median. What does the median tell you?
b. Do any of the 16 households have the median number of children? Explain.
2. a. What is the mean number of children per household for the 16 households? Explain how to find the mean. What does the mean tell you?
b. Do any of the 16 households have the mean number of children? Explain.
For exercises 3&4, the mean number of people per household for eight households is 6 people. 3. What is the total number of people in the eight households? a) 11 b) 16 c) 48 d) 64 4. a. Make a line plot showing one possible arrangement for the numbers of people in the eight households. (Remember, the MEAN is 6.)
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Page 30 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
b. Make a line plot showing a different possible arrangement for the numbers of people in the eight households. (Remember, the MEAN is 6.)
c. Are the medians the same for the two arrangements you made?
5. The students in Mr.Wilson’s study hall spent the following amounts of time on their HW. 3 4
ℎ𝑜𝑢𝑟
1 2
ℎ𝑜𝑢𝑟
1
1 4 ℎ𝑜𝑢𝑟𝑠
3 4
1
ℎ𝑜𝑢𝑟
2
ℎ𝑜𝑢𝑟
What is the mean time his students spent on HW?
6. Use the data from question 5. What is the median time Mr. Wilson’s students spent on HW? a)
1 2
ℎ𝑜𝑢𝑟
b)
3 4
ℎ𝑜𝑢𝑟
c) 1 hour
1
d) 1 4 ℎ𝑜𝑢𝑟𝑠
7. Six students each had a different number of pens. They put them all together and then distributed them so that each student had the same number of pens. a. Choose any of the following that could be the number of pens they had altogether. Explain your reasoning. A. 12 B. 18 C. 46 D. 48
b. Use your response from part a. How many pens did each person have after the pens were distributed evenly?
c. Your classmate says that finding the mean number of pens per person is the same as finding the number of pens each person had after the pens were distributed evenly. Do you agree or disagree? Explain.
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Page 31 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Box Plots (aka Box-and-Whisker Plots) WARMUP: 1. Create a set of data with 5 data values that have a median of 4.
2. Create another set of data with 5 data values that have a median of 4.
3. Do you use any “tricks” to help with these questions?
4. Create a set of data with 6 data values that have a mean of 5.
5. Create another set of data with 6 data values that have a mean of 5.
6. A trick in creating a set of data with the same mean is:
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Page 32 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Box Plots (aka Box-and-Whisker Plots)
FIVE MAGIC NUMBERS 1. The ______________ _______________ is the smallest data value. This starts the first “whisker.”
2. The ______________ _______________ is the middle of the lower half of the data. _______% of the data values are below this number and ________% are above. This ends the first “whisker” and starts the “box.”
3. The ______________ is the middle of all of the data. _______% of the data values are below this number and ________% are above. This is a vertical line inside the “box.”
4. The ______________ _______________ is the middle of the upper half of the data. _______% of the data values are below this number and ________% are above. This ends the “box” and starts the last “whisker.”
5. The ______________ _______________ is the largest data value. This is the end of the last “whisker.” **The INTER-QUARTILE RANGE is the __________ of the ___________. This is the middle half (50%) of the data. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ NOW, here’s a set of data….you have to ______________ it to find the 5 magic numbers!
8, 20, 12, 16, 18, 22, 24, 14, 25, 20, 21 Rewrite the numbers:
Circle the five magic numbers in the list you made! Now, put each point above the number line below. Make your box and whiskers!
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Page 33 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Here’s another set of data….do it again!
16, 18, 12, 10, 14, 10, 8, 12 Rewrite in order from least to greatest:
What do I do for the five magic numbers if they are “between” data values?
Find the five magic numbers from the data set above.Then make your box-and-whisker plot.
Analysis:
25% of the data is below _________. 50% of the data is above _________. 75% of the data is below _________. 50% of the data is between ___________ and _________. 50% of the data is in the ___________________. 50% of the data is in the ___________________. How can a box-and-whisker plot help you to understand a set of data? _________________ What is the Inter-Quartile Range (IQR)?
If there are 12 numbers in a set of data, how many numbers are in each part of the box-andwhisker plot?
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Page 34 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
16. Create 2 box plots above the number line below (one for each set of data).Label them! Midwestern States (area in 1,000 mi2): 45, 36, 58, 97, 56, 65, 87, 82, 77 Southern States (area in 1,000 mi2): 52, 59, 48, 52, 42, 32, 54, 43, 70, 53, 66
What conclusions can you make by looking at the plots above? 34
Page 35 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Warmup: For the following types of data, which measure of central tendency is BEST—mean, median, or mode? Explain. 1. most popular movie in the last month
2. favorite hobby
3. class sizes in a school
4. ages of members in a club
****CHALLENGE**** Each person has taken four tests and has one more test to take. Find the score that each person must make to change the mean or median as shown. 5. Barry has scores of 93, 84, 86, and 75. He wants to raise the mean to 86. Hint: When you find the mean, first you add, then divide…now undo (first multiply then subtract).
6. Liz has scores of 87, 75, 82, and 93. She wants to raise the median to 87. Hint: 87 will be the MIDDLE point (like the fulcrum on a balanced scale).
7. Li’s bowling scores are: 129, 136, 201, 146, 154. Make a box plot (find those 5 magic numbers and graph them). What is the IQR?
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Page 36 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Mean Absolute Deviation (MAD) MAD NOTES: Describing Data through Measures of Center & Spread
There are two ways to describe a set of data:__________________ & ____________________ Today we will focus on the numerical descriptions. MEASURES OF CENTER
Mean:
A numerical measure of center that is the arithmetic average of the data. Affected by
outliers. Mean:
𝑥̅ =
𝑡ℎ𝑒 𝑠𝑢𝑚 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑡𝑎
=
∑𝑥 ∑𝑛
Symbols to represent the mean. The large “E” type symbol indicates a “sum”. So the top is the sum of the data numbers and the bottom is the sum of how many pieces of data there are.
Median:
A numerical measure of center that describes the middle value of a data set. The median is not affected by outliers. Note that the median does not have to be one of the values in the data set, but a value that divides the data set in half so that 50% of the data values lie above the median and 50% of the data set lie below the median.
MEASURES OF SPREAD describe________________________________________________ ______________________: ______________________:
MEAN ABSOLUTE DEVIATION
EXAMPLE
STEP 1:
STEP 1
STEP 2
DATA
DIFFERENCE Data minus Mean
STEP 2:
STEP 3:
MEAN:
STEP 4:
STEP 4
36
STEP 3
ABSOLUTE VALUE
Page 37 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017 _________________________________: A numerical measure of spread that shows how much data values vary from the mean. A low mean absolute deviation indicates that the data points tend to be very close to the mean and not spread out very far so the mean is an accurate description of “typical”, and a high mean absolute deviation indicates that the data points are spread out over a large range of values. BACK TO PPT SLIDE 9…..
Li
Bessie
Jamal
MEAN:
MEAN:
MEAN:
DATA
DIFFERENCE
ABSOLUTE VALUE
DATA
Data minus Mean
DIFFERENCE
ABSOLUTE VALUE
DATA
Data minus Mean
DIFFERENCE Data minus Mean
Who do you think is it BEST STUDENT? Explain.
MAD: Data Set:
MAD: 30, 38, 40, 42, 48 DATA
Find the mean:
DIFFERENCE
̅ =MAD: 𝒙 _________
ABSOLUTE VALUE
Data minus Mean
SUM of Values:
Mean Absolute Deviation (MAD) = 37
ABSOLUTE VALUE
Page 38 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Mean Absolute Deviation Homework Find the mean absolute deviation for each set of data. 1. 80, 82, 82, 88, 90, 94, 102, 104, 106 MEAN:
MAD:
DATA
DIFFERENCE
ABSOLUTE VALUE
Data minus Mean
5. 160, 166, 170, 172, 178, 180, 190, 204, 260 MEAN:
MAD:
More MAD and measures of variability DATA DIFFERENCE
ABSOLUTE VALUE
Data minus Mean
The following data set represents the size of 9 families. Sum =
Sum =
3, 2, 4, 2, 9, 8, 2, 11, 4 What is a mean? ________________________________________________________________ What is the mean for this set of data? __________ What is mean absolute deviation? the ____________
_____________of each data value from the _____________
What is the MAD for this data set? Make a chart and figure it out! MAD = _________
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Page 39 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
3
4
5
6
7
8
9
Based on the picture above, what are the “FIVE MAGIC NUMBERS” and what do they mean? 1. 2. 3. 4. 5.
Looking at the boxplot below, name and give the value of the FIVE MAGIC NUMBERS.
1. 2. 3. 4. 5.
39
Page 40 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Variability To find a RANGE you need which two “MAGIC NUMBERS?”
To find the InterQuartile Range (IQR), you need which two “MAGIC NUMBERS?”
Use the data displayed in the box plots below to answer the questions. Amount Spent by Each Customer (in dollars) at Casual Café
Amount Spent by Each Customer (in dollars) at Bountiful Bistro
1) Find the following for each set of data. a. median b. range c. interquartile range
2) Use the medians of the data to compare the amounts spent by customers at each restaurant.
3) Use the ranges and interquartile ranges of the data to compare how amounts spent by customers at each restaurant vary. Which restaurant would you rather eat at based on this data? Explain. 4) Is there symmetry or lack of symmetry in each box plot?
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Page 41 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Measures of Variability: MAD and IQR Variability means ______________________________________________________________ Why is MAD a measure of variability?
Why is IQR a measure of variability?
Math Exam Grade Amount of Review Before the Exam
Review Class
No Review
Grade as a Percent 1) What conclusions can you draw from looking at the plot about how effective the math exam review class was? 2) What is the difference in the medians between the sets of data?
3) The mean absolute deviation for both groups of students is 6.2. Compare that value to the difference in medians. What does that tell you about the data?
4) What is the interquartile range for each set of data? What does that tell you about the data?
CHALLENGE: Determine which 2 sets of data will overlap more. Set A has a mean of 12 and a mean absolute deviation of 5.1. Set B has a mean of 23 and a mean absolute deviation of 4.9. Set C has a mean of 10 and a mean absolute deviation of 4.8. Day 9 HW (MAD and IQR = Measures of Variability)
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Page 42 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Directions: Solve the following problems by finding the median, interquartile range (IQR), or range. You may use a calculator, but you must show your work! 1.
{13, 15, 9, 35, 25}
Median =
________
Q1 =
________
Q3 =
________
IQR =
________
2.
{6, 1, 3, 8, 5, 11, 1, 5}
Median =
________
Q1 =
________
Q3 =
________
IQR =
________
3.
Jason and Jill are two students in Mr. White’s math class. On the last five quizzes, Jason scored an 80, 90, 95, 85, and 70. Jill scored a 70, 75, 90, 100, and 95. Find the median and IQR for each student.
Jason’s Median :______
Jill’s Median = _______
Jason’s IQR = ______ Jill’s IQR = ________ Whose quiz grades are more consistent? _______
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Page 43 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Find the mean absolute deviation for each set of data. Round to the nearest hundredth if necessary. Then describe what the mean absolute deviation represents.
4. Number of Daily Visitors to a Web Site 112 145 108 160 122
5.
Mean = ___________ Data Values
Difference from Mean
Zoo Admission Prices ($) 9.50 9.00 8.25 9.25
8.00
8.50
Mean = ___________ Data Values
Absolute value
Difference from Mean
MAD = ________
MAD = ________
6.
7.
43
Absolute Value
Page 44 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
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Page 50 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
More practice with Histograms and Box Plots Multiple Choice. Identify the choice that best completes the statement or answers the question. ____ 1. The number of pieces of candy in randomly selected jars are 20, 1, 29, 21, 40, 52, 41, 44, 60, 67. Display the data using a histogram. a.
Pieces of Candy in Jars
c.
Pieces of Candy in Jars
9
8
8
Frequency
10
9
Frequency
10
7 6 5
7 6 5
4
4
3
3
2
2
1
1
1–20
b.
21–40 41–60 Pieces of candy
61–80
Pieces of Candy in Jars
1–20
d.
8
Frequency
9
8
Frequency
10
9
6 5
7 6 5
4
4
3
3
2
2
1
1
1–20
21–40 41–60 Pieces of candy
61–80
1–20
21–40 4–-60 Pieces of candy
____ 2. Display the data using a histogram. The numbers of students in different classes at a community college: 25, 15, 28, 52, 22, 38, 42, 44, 24, 32, 19, 28, 29, 20, 31 a. c.
Community College Class S izes
7
6
6
Frequency
Frequency
Community College Class S izes
7
5 4 3
61–80
Pieces of Candy in Jars
10
7
21–40 41–60 Pieces of candy
5 4 3
2
2
1
1
15-24
15-19 20-29 30-39 40-54 S tudents
50
25-34 35-44 S tudents
45-54
61–80
Page 51 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017 b.
d. Community College Class S izes
Community College Class S izes
7
7
6
Frequency
Frequency
6 5 4
5 4 3
3 2
2 1
1
15-24
15-24 25-34 35-44 45-54 S tudents
____ 3.
25-34 35-44 45-54 S tudents
The number of laps around a track for five runners are 14, 8, 7, 4, 11. Display the data using a box-and-whisker plot.
a. 0
2
4
6
8
10
12
14
16
18
20
22
24
0
2
4
6
8
10
12
14
16
18
20
22
24
0
2
4
6
8
10
12
14
16
18
20
22
24
0
2
4
6
8
10
12
14
16
18
20
22
24
b.
c.
d.
____ 4.
Make a histogram for the numbers of students in different classes at a community college.
25, 15, 28, 52, 22, 38, 42, 44, 24, 32, 19, 28, 29, 20, 31 a.
c. Community College Class S izes
7
7
6
6
Frequency
Frequency
Community College Class S izes
5 4 3
5 4 3
2
2
1
1
15-24
25-34 35-44 S tudents
45-54
15-24
51
25-34 35-44 45-54 S tudents
Page 52 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017 b.
d. Community College Class S izes
7
7
6
6
Frequency
Frequency
Community College Class S izes
5 4 3
5 4 3
2
2
1
1
15-19 20-29 30-39 40-54 S tudents
15-24 25-34 35-44 45-54 S tudents
____ 5. The number of calls answered by a paramedic team over an 8-day period are given. Use the data to make a box-and-whisker plot. 12, 6, 8, 15, 14, 6, 14, 10 a. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
b. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
c. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
d. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
____ 6. Average prices for 35 different models (types) of car from the 3 most popular automobile brands in the United States are shown. Make a dot plot of the data and explain what the distribution means. Average Suggested Retail Prices, 2011 Automobile Models (in thousands of dollars) Price Range
10- 14.9
15- 19.9
20- 24.9
25- 29.9
30- 34.9
35- 39.9
40- 44.9
45- 49.9
# of Models Price Range
1 50- 54.9
3 55- 59.9
5 60- 64.9
6 65- 69.9
9 70- 74.9
2 75- 79.9
2 80- 84.9
3
# of Models
2
0
0
1
0
0
1
a.
This data distribution is skewed to the left. Most car models cost less than the mean.
52
Page 53 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017 b.
The data distribution is skewed to the right. Most car models cost more than the mean. c.
The data distribution is skewed to the right. Most car models cost more than the mean. d.
This data distribution is skewed to the left. Most car models cost less than the mean.
____ 7.
The high temperatures in Concord, CA, for October 1–15, 2005, are given below.
Look at the histogram of these data below. What is the error in this histogram?
a. The bar for 74–77 is too short. b. The bar for 78–81 is too tall.
c. The bar for 82–85 is too tall. d. The bar for 86–89 is too short.
53
Page 54 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017 ____ 8.
The high temperatures for Concord, CA, for October 1–15, 2005, are given below.
Look at the box-and-whisker plot of these data below. What, if anything, is wrong with this box-and-whisker plot?
66
68
70
72
74
76
a. The value of Q1 is incorrect. b. The median is incorrect. ____ 9.
78
80
82
84
86
88
90
c. The value of Q3 is incorrect. d. The box-and-whisker plot is correct.
The ages of the U.S. Presidents that were inaugurated during the 1900s are given below.
Look at the box-and-whisker plot of these data below. What, if anything, is wrong with this box-and-whisker plot?
a. The value of Q1 is incorrect. b. The median is incorrect. ____ 10.
c. The value of Q3 is incorrect. d. The box-and-whisker plot is correct.
Which data set could be used to create the box-and-whisker plot shown below?
a. {4, 4, 4, 4, 6, 6, 8, 9, 11, 11, 11} b. {3, 4, 4, 4, 5, 7, 8, 10, 11, 12, 13}
c. {2, 3, 4, 4, 5, 7, 8, 9, 11, 13, 14} d. {3, 3, 3, 4, 7, 7, 11, 11, 13, 13, 13}
54
Page 55 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017 ____ 11. A weatherperson records how much rain, in inches, falls each day in the first week of a month. She makes a box-and-whisker plot of the data, shown below.
Which could be the data the weatherperson recorded? a. {0, 1, 1, 2, 4, 4, 6} b. {0, 0, 1, 2, 2, 4, 6} ____ 12. An oceanographer is measuring high tide against a mark he’s made on a post. The results of several days of measurements are shown below.
Which data set shows the heights of high tide over this period? a. { c. { , , 0, 0, 0, 0, 1, 1, 3.5} , , b. { d. , , , 0, 0, 1, 1, 2, 3.5} { , , ____ 13.
, ,
, 0, 0, 0.9, 1.1, 3.5} , 0, 1.5, 2, 2.5, 3.5}
Make a box-and-whisker plot of the data. Find the interquartile range.
a. 6
7
8
9 10 11 12 13 14 15 16 17 18 19
Interquartile range: 5.5 b. 6
7
8
9 10 11 12 13 14 15 16 17 18 19
Interquartile range: 5 c. 6
7
8
9 10 11 12 13 14 15 16 17 18 19
Interquartile range: 5.5 d. 6
7
8
9 10 11 12 13 14 15 16 17 18 19
Interquartile range: 5
55
Page 56 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017 ____ 14. Marisa recorded the heights, in inches, of the 17 students in her homeroom. The data set she gathered was 66, 63, 60, 55, 73, 59, 59, 63, 71, 61, 65, 64, 64, 69, 65, 66, 64. She created a histogram to display the data. Which of the following are possible intervals she could use in her histogram? a. 60-64, 65-69, 70-74 b. 55-59, 60-66, 67-69, 70-74 c. 55-59, 60-64, 65-69, 70-74 d. 60-69, 70-79 ____ 15. Seung used box-and-whisker plots to show the points he scored in his basketball games this season. He used different plots for the home and away game data, and produced the graph below.
0
2
4
6
8 10 12 14 16 18 20 22 24 26
Unfortunately, Seung cannot remember which plot represents the home game data and which represents the away game data. Which fact can he use to determine which set of data was used to create each box-andwhisker plot? a. Seung scored at least 5 points in every home game. b. The mode of the set of away game scores was 14. c. Seung scored 23 points in an away game last week. d. Seung played more home games than away games.
____ 16. Shawn collected the heights, in inches, of his classmates. He rounded the measurements to the nearest inch and used those values to create a dot plot. The next day, Shawn revisited the data he gathered about his classmates’ heights, rounded each measurement to the nearest multiple of 5 inches, and used this set of rounded data to create a second dot plot. Which characteristic of the two dot plots must be the same for both sets of data? a. the highest data value b. the number of data points plotted c. the lowest data value d. the range of the data
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Page 57 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
Unit 13 STUDY GUIDE Analyze a set of data (Show all work if necessary): 1.
# of slices of pizza eaten by a 16-year old boy in one sitting: Mean =__________ Median =__________
7, 5, 6, 7, 5, 5, 8, 15
Mode =_________
Range =________
Do you think there’s an outlier? ___________ Which measure of “center” is best for this set of data?________________ 2. Use the data in the table to make a frequency table with intervals. Then use the frequency table to make a histogram.
Miles per Gallon of Vehicles on the Interstate 12
45
31
9 32
19
27
23
34
29 17 25 28
Complete the frequency table:
Complete the histogram: 6
Miles per Gallon of Vehicles on I-95
Miles per Gallon
F R E Q U E N C Y
Frequency
1-10 11-20
5 4 3 2 1
1-10
11-20
3. Describe the shape of the data in the histogram.
4. Based on the shape of the data, which interval has the median and mean? _______________ 5. Create a line plot for this set of data:
8, 11, 5, 8, 9, 6, 8, 7, 10
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Page 58 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
6. From the $ Spent on Snacks line plot above:
7. From the Shoe Sizes line plot above:
a)
Find the range: _________
a) Find the mean: ________
b)
Find the median: _________
b) Find the mode: ________
Answer questions 8-10 using the box-and-whisker plots below.
The top box plot shows # of
pencils in students’ backpacks. The bottom box plot shows the # of
pens in students’ backpacks. 8.
What percent of students had more than 7 pencils in their backpacks?
9.
What percent of students had less than 10 pens in their backpacks?
10. What do the box-and-whisker plots tell you about students carrying around pens and pencils in their backpacks? Interpret the data on the graphs. 11.
Create a box-and-whisker plot from the following set of data:
Minimum=_______
Q1=________
0 12.
1
Median=________
2
3
4
5
8, 2, 9, 4, 6, 8, 5
Q3=________
6
7
8
Maximum=_______
9
What is the interquartile range (IQR) of this set of data? ____________ 58
Page 59 CCM6 & CCM6+ UNIT 13 Statistics and Data 2016-2017
13.
Student heights in inches: 65, 62, 59, 60, 64, 70 Find the mean absolute deviation of student heights. Fill in the table below to find it: Mean height = _______ M. A. D. = _______
DATA
DIFFERENCE from MEAN
Absolute Value
65 (Round to the nearest hundredth if necessary)
62 59
If a data set has an outlier, the MAD will be ____________ than a data set with data values that are all very close together.
60 64 70
59
