Question

Assignment 3: Data Analysis with Graphs Assignment

• Data Set A Masses, to the nearest kilogram, of 30 men: 74 52 67 68 71 76 86 81 73 64 75 71 57 67 57 59 72 79 64 70 77 79 65 68 76 83 61 63 68 74
• Data Set B Times, in seconds, taken by 20 boys to swim one length of a pool 32 31 26 27 27 32 29 26 25 25 31 33 26 30 23 32 27 26 31 29

1. how would you draw a stem and leaf diagram for each of the above data sets.

2.Using your stem and leaf diagrams, make at least 2 comments about each set of data (i.e., what does the diagram tell you about the data?).

3.For each of the data sets:

a.Create a histogram from the data.

b.Does the histogram tell you anything that wasn’t evident from the stem and leaf diagram? Does it make anything about the data more difficult to see?

c.Create a second histogram with a different bin width. How does this change how you interpret the data?

4.For each of the data sets, explain whether you prefer the stem and leaf diagram or a histogram and why?

Answer 1

1. Stem-leaf plot for A

5 | 2
5 | 779
6 | 1344
6 | 577888
7 | 0112344
7 | 566799
8 | 13
8 | 6

Stem-leaf plot for B

2 | 3
2 | 55666677799
3 | 01112223

2. For dataset A, values run from 52 to 86. The distribution underlying A is seem to be skewed negatively

For dataset B, values run from 23 to 33. The distribution underlying A is seem to be skewed positively

3. Histogram of A with class intervals 50-58, 58-66..

Histogram of B  with class intervals 20-25,25-30...

The histograms convey the same message as the stem leaf disgram. However, getting the maximum and minimum from these histograms is not possible.

.

4. Histogram of A with class intervals 50-55, 55-60..

Histogram of B with class intervals 22-25,25-28,..

.

The same information is conveyed when different bins are used to construct the histograms.

4. Since, the data set is small, using stem-leaf disgram would be more helpful in getting the magnitudes (e.g. maximum, minimum) of the observations , whereas use of histogram does not give the magnitudes and provides the number of values in each bin and is less informative.