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Question

There is a grouped data distribution for which mean is to be found by step deviation method. For this purpose, the below table is constructed. Fill in the blanks

Class IntervalNumber of Frequency(fi)Class mark(xi)di=xiaui=dih01004050200D......10020039150B.....E.....200300342500030040030350100140050045450C.....F......TotalA.fi=......

The A, B, C, D, E and F respectively are


  1. 188 , -100, 200, -2 ,-1 and 2

  2. 186 , 100, -200, -2 ,-1 and 2

  3. 188 , 100, -200, 2 ,-1 and -2

  4. 186 , -100, -200, -2 ,-1 and 2


Solution

The correct option is A

188 , -100, 200, -2 ,-1 and 2


fi= sum of frequencies of each class = 40 + 39 + 34 + 30 + 45 = 188

di = xi - a

where xi = ith class mark

a = assumed mean

Using above formula for 1st class(0-100) we get-

-200 = 50 – a

a = 250

Using above formula for 2nd class(100-200) we get-  

B = 150 – 250 

B = -100

Similarly, C = 200.

 ui = (di)h

Here h = class interval = 100. h is constant.

For 1st class(0-100),

 u1 = d1h= -200/100 = -2

Thus, D = -2

Similarly E = -1, F = 2 


Answers are 188 , -100, 200, -2 ,-1 and 2

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