A. To construct a grouped frequency distribution for the given data, we first need to determine the range of the data:
Range = Maximum value - Minimum value
Range = 39 - 5
Range = 34
Next, we need to decide on the width of each class interval. A common rule is to choose the number of classes to be between 5 and 20, and then choose a class width that is a convenient number. In this case, we will choose 8 classes and a class width of 5.
Class width = Range / Number of classes
Class width = 34 / 8
Class width ≈ 4.25
We can round up the class width to 5 to get a convenient number. The class intervals are:
5 - 9.99
10 - 14.99
15 - 19.99
20 - 24.99
25 - 29.99
30 - 34.99
35 - 39.99
40 - 44.99
Next, we count the number of observations that fall into each class interval. This gives us the frequency of each interval. The grouped frequency distribution is:
Class Interval Frequency
5 - 9.99 5
10 - 14.99 8
15 - 19.99 9
20 - 24.99 16
25 - 29.99 7
30 - 34.99 6
35 - 39.99 1
40 - 44.99 0
B. To draw the histogram, frequency polygon, and cumulative frequency curves, we first need to calculate the cumulative frequencies. The less than cumulative frequency is the running total of the frequencies up to each class interval, while the more than cumulative frequency is the running total of the frequencies from each class interval to the end.
Class Interval Frequency Less than Cumulative Frequency More than Cumulative Frequency
5 - 9.99 5 5 62
10 - 14.99 8 13 57
15 - 19.99 9 22 49
20 - 24.99 16 38 40
25 - 29.99 7 45 24
30 - 34.99 6 51 17
35 - 39.99 1 52 11
40 - 44.99 0 52 10
Now we can draw the graphs:
Histogram:
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5 10 15 20
Frequency polygon:
25 |
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