Question

Find the means of the following data using the step deviation method
class interval 5-15, 15-25, 25- 35, 35- 45, 45-55, 55- 65, 65- 75
frequency. 6, 10, 16, 15, 24, 8, 7.​

Answer 1

Answer:

Let us choose a = 40, h = 10, then and

di=xi–40andui=xi-4010

Using step-deviation method, the given data is shown as follows:

Class Frequency (fi) Class mark (xi) di=xi – 40

ui=xi−4010 (fiui)

5 – 15 6 10 -30 -3 -18

15 – 25 10 20 -20 -2 -20

25 – 35 16 30 -10 -1 -16

35 – 45 15 40 0 0 0

45 – 55 24 50 10 1 24

55 – 65 8 60 20 2 16

65 – 75 7 70 30 3 21

Total ƩƩfi = 86 ƩƩfiui= 7

The mean of the data is given by,

x = a+

(∑ifiui∑ifi)×h

= 40 +

786×10

=

40+7086

= 40 +0.81

= 40.81