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Question

For the given distinct values x1,x2,x3,.....xn occurring with frequencies f1,f2,f3,...fn respectively. The mean deviation about mean where ¯x is the mean and N is total number of observations would be


A

1Nni=1fi |xiM|

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B

1Nni=1fi|xi¯x|

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C

ni=1|xi¯x|N

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D

Nfini=1|xi¯x|

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Solution

The correct option is B

1Nni=1fi|xi¯x|


Clearly mean of the given distribution will be
x=ni=1fi xini=1 fi

To find the mean deviation about ¯x we need sum of absolute deviation about ¯x for each xi

Which would be ni=1fi(xix|

Total number of observations = ni=1 fi = N

Mean deviation about mean = =1Nni=1fi(xix|

option b


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