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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:
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.
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.
1) Mean
The mean is given by the sum of the data divided by the number of data (4, in this case):
2) Standard deviation
The standard deviation is given by:
where
is the mean, that we already found at point 1), and N=4. Substituting data, we have:
The mean is given by the sum of the data divided by the number of data (4, in this case):
2) Standard deviation
The standard deviation is given by:
where