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.
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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
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