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Question

With reference to the impact of outlier on mean, which of the following option is correct?

A
The value of mean remains unaffected with or without outlier.
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B
The presence of outlier may increase or decrease the value of mean.
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C
The presence of outlier in the data set always increases its mean.
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D
None of the above.
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Solution

The correct option is B The presence of outlier may increase or decrease the value of mean.
Consider the data set for the number of states visited by students as follows:


In the given data, all the values lies within the range of 0 to 6, except for 18 which is quite different from the other values. Thus, 18 is said to be the outlier of this data set.

The mean of this data is calculated as,

Mean=Sum of all data valuesTotal number of data values

Thus, the mean with and without outlier will be given as,

Mean with outlier=4+3+6+2+0+3+4+6+5+5+4+18+1+214=6314=4.5 Mean without outlier=4+3+6+2+0+3+4+6+5+5+4+1+213=4513=3.5

Hence for this data set, the presence of outlier increases the value of mean.

Now, consider another data set showing the age of 5 people.


In this data set, all the values lies within 34 to 36, except for 12 which is quite different from the range of other values. Thus, 12 is said to be the outlier of this data set.

Here, the mean with and without outlier will be given as,

Mean with outlier=34+33+12+35+365=1505=30 Mean without outlier=34+33+35+364=1384=34.5

Hence for this data set, the presence of outlier decreases the value of mean.

Thus, the presence of outlier may increase or decrease the value of the mean of a given data set.

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