Which class has the greatest frequency and which has the least ?

14  5  7  5  18  6  11  15  12  3  0  6  1  7  18  1  1  19  17  14
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1 Answer

First, put these in order with their frequency if more than one).

0, 1 (3), 3, 5 (2), 6 (2), 7 (2), 11, 12, 14 (2), 15, 17, 18 (2), 19

The values range from 0 to 19, so the natural way to classify them would be to split them into 0-3, 4-7, 8-11, 12-15, 16-19. We have:

Class 1: 0 1 1 1 3; Median: 1

Class 2: 5 5 6 6 7 7; Median: 6

Class 3: 11; Median: 11

Class 4: 12 14 14 15; Median: 14

Class 5: 17 18 18 19; Median: 18

The medians are the midpoints of the data in each class. Below are the data values 0 to 19 and their absolute frequencies followed by their relative and cumulative frequencies.

Class 1

0 1 0.2 0.2

1 3 0.6 0.8

2 0 0 0.8

3 1 0.2 1.0

Class 2

4 0 0 0

5 2 0.33 0.33

6 2 0.33 0.67

7 2 0.33 1.00

Class 3

8 0 0 0

9 0 0 0

10 0 0 0

11 1 1 1

Class 4

12 1 0.25 0.25

13 0 0 0.25

14 2 0.5 0.75

15 1 0.25 1.00

Class 5

16 0 0 0

17 1 0.25 0.25

18 2 0.50 0.75

19 1 0.25 1.00

Class 2 has the greatest frequency (6) and class 3 the least (1).

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