  Question

There is a grouped data distribution for which mean is to be found by step deviation method. Class IntervalNumber of Frequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200D......100−20039150B.....E.....200−3003425000300−400303501001400−50045450C.....F......TotalA=∑fi=...... Find the value of  A, B, C, D, E and F respectively.

A

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

186 , 100, -200, -2 ,-1 and 2  C

188 , 100, -200, 2 ,-1 and -2  D

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 ∴A=188 Now, di=xi−a where, xi is ith row class mark and 'a' is assumed mean. Using above formula for 1st class (0-100) we get: −200=50−a⇒a=250 and class size h=100 Using the above information, lets complete the table,. Class IntervalNumber of Frequency(fi)Class mark(xi)di=xi−aui=dih0−1004050−200−2100−20039150−100−1200−3003425000300−400303501001400−500454502002TotalA=∑fi=188 Thus,A, B, C, D, E and F are 188,−100,200,−2,−1 and 2 respectively. Mathematics

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