Practice 1.2 – Graphing Quantitative Data Goal: To construct dot and stem plots by hand and describe distributions. 1. Use each graph to describe the distribution of the data set. Use “SOCS” as a guideline. a)
b)
Shape: right-skewed, (and unimodal) Outliers: none (not obvious) Center: median is 6.5 Spread: range: 4 (5 to 9)
c)
Shape: left skewed Outliers: 45 Center: median: 50 matches per box Spread: range: 7 (45 to 52)
Shape: roughly uniform Outliers: none Center: median: 54 Spread: range 96 (2 to 98)
d) Number of Home Runs on Friday, June 3, 1994, in the American League:
Shape: roughly symmetric Outliers: none Center: median: 57.5 (between 57 and 58) Spread: range: 42 (35 to 77)
2. 17 students were asked how many text messages they had sent on a particular day. 0
3 2
0 4
5 4
3 3
1 4
6 3
0 3
2 9
a) Create a frequency table. Number of text messages 0 1 2 3 4 5 6 9 b) Create a
Frequency 3 1 2 5 3 1 1 1 dot plot.
Number of Text Messages
c) Describe the distribution of text messages.
The distribution is roughly right skewed. There is an outlier of 9 text messages. The median number of text messages is 3. The number of text messages has a range of 9 (0 to 9). 3. The heights, in cm, of 20 people are as follows:
154, 143, 148, 139, 143, 147, 153, 162, 136, 147, 144, 143, 139, 142, 143, 156, 151, 164, 157, 149, 146 a) Create a stem plot and include a key. b) Describe the distribution of heights. The distribution is slightly right skewed (note that a split stem Key: 13|6 = 136 and leaf plot would confirm this). There are no outliers. The median height is 147 cm and the heights have a range of 28 cm (136 cm to 164 cm).
4. The data below give the amount of caffeine content (in milligrams) for an 8-ounce serving of popular soft drinks. 20 16
15 38
23 36
29 35
23 37
15 27
23 33
31 37
28 25
35 47
37 27
27 29
24 26
26 43
47 43
28 28
24 35
28 31
28 25
a) Create a split stem plot.
b) Why is a split stem plot a better choice than a regular stem plot? It shows that the distribution is bimodal, which could not be seen with the regular stem plot. c) Describe the distribution. The distribution is bimodal, with no outliers. A typical amount of caffeine is 28 mg. The range is 32 mg (15 mg to 47 mg).
5. The following data show the amount of cash ($) carried by a random sample of teenage boys and girls. Boys:
Girls:
41 48
35 71
49 59
42 24
11 42
42 65
26 38
73 34
7 54
53 68
21 62
57
44 34 22 33 36 11 43 34 36 26 46 38 54 39 28
a) Create a back-to-back stem plot. Boys Girls 7 0 1 1 1 641 2 268 854 3 3446689 982221 4 436 9743 5 4 852 6 31 7 b) Compare the distributions. The distribution for girls is symmetrical but boys is slightly LEFT-skewed (remember mirror image). There are no outliers for either gender. The boys carried more cash than the girls – a median of $42 for the boys versus $36 for the girls. There was more variation among the boys, with a range of $64 as opposed to the girls, who have a range of $43.
