Question

If you are given the following stem and leaf display and asked to construct a frequency distribution chart, what would be the width of the intervals?
1-332

2-45

3-1157

4-231

5-2112

Answer 1

Answer:

Width of intervals: 8

Step-by-step explanation:

We first look at how data is represented in a stem-leaf diagram.

Any number of the left (before -) is the stem and all numbers on right (after -) are the leaves. Each combination of stem and leaf represents one number. For example: 1 - 332 represents: 13, 13, 12.

Our data is as follows:

13, 13, 12, 24, 25, 31, 31, 35, 37, 42, 43, 41, 52, 51, 51, 52

To calculate the width of the frequency distribution chart, we have the following formula:

$Class\ width = \frac{Range}{Number\ of\ classes}$

The range of any data set = Maximum value in the data set - Minimum value in the data set

Maximum value in this case as seen from the data is 52 and minimum is 12.

Range = 52 - 12 = 40

Since we had only 5 stems in the data, we shall use that as the number of classes required in the frequency distribution chart.

$Class\ width = \frac{40}{5} = 8$

Hence, the class width in this data set will be 8.

To make the intervals, we begin from the minimum value and add 8 to it. The intervals will be:

12 - 20

20 - 28

28 - 36

36 - 44

44 - 52

Observe, that all the values of the stem lie within each interval.

For example, there are 3 values for stem 1: 12, 13, 13 and each lie in the first interval 12 - 20.

Next, the values of stem 2 are 24 and 25. Each of these value lie in the second interval 20 - 28; and henceforth.