Question

If one number in a data set is changed, will this affect the mean of the given collection of data? ​

Answer 1

Given :       One number in a data set is changed

To  Find : will this affect the mean of the given collection of data

Solution:

Mean =  Sum of all observations / number of observations

If   One number in a data set is changed then Sum of observation is changed

but number of observations are same

Hence Mean will be changed by change in observation / number of observations

Example  

2  3   5   7   8

Mean = (2 + 3 + 5 + 7 + 8)/5 = 25/5 = 5

3 is changed to 4

=> Mean = ( 2 + 4 + 5 + 7 + 8)/5 = 26/5 = 5.2

If Data is grouped data then mean is not changed if changed data is still in the same group

but Mean is changed if changed number is in other group

If one number in a data set is changed this will affect the mean of the given collection of data

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