Question

Classify the following data by taking class interval such that their mid-values are 17, 22, 27, 32 and so on:

30 30 36 33

42 27 22 41

30 42 30 21

54 36 31 16

40 28 19 17

48 28 48 36

14 37 16 37

17 54 42 41

51 44 32 46

42 31 21 47

25 36 22 52

41 40 40 53

Answer 1

The class interval can be calculated from the mid-points using the following adjustment formula.

The value obtained is then added to the mid point to obtain the upper limit and subtracted from the mid-point to obtain the lower limit.

For the given data, the class interval is calculated by the following value of adjustment.
$\mathrm{Value}\mathrm{of}\mathrm{adjustment}=\frac{17-12}{2}=2.5$

Thus, we add and subtract 2.5 to each mid-point to obtain the class interval.

For instance:

The lower limit of first class = 12 – 2.5 = 9.5

Upper limit of first class = 12 + 2.5 = 14.5

Thus, the first class interval is (9.5 − 14.5). Similarly, we can calculate the remaining class intervals.

Mid-value	Class-interval	Frequency (f)
12 17 22 27 32 37 42 47 52	9.5 − 14.5 14.5 − 19.5 19.5 − 24.5 24.5 − 29.5 29.5 − 34.5 34.5 − 39.5 39.5 − 44.5 44.5 − 49.5 49.5 − 54.5	1 5 4 4 8 6 11 4 5
		∑f = 48