Question

When an observation that is much larger than the rest of the data is added to a data set, the value of the mean will _.

Answer 1

Increase. Any outliers will affect the mean drastically.

Answer 2

Answer: Affect extremely.

Explanation:

When a data set contains extreme values also known as outliers , then mean gets affected extremely.

For example : We have a data set with values : 1 , 2, 1,2,1, 2, 12

Here , 12 is much larger than the rest of the data values.

Mean of data :
`\frac{\text{Sum of observations}}{\text{Number of observations}}`

`=(1 +2+ 1+2+1+2+12)/(8)=(21)/(8)=2.625`

Mean excluding outlier :

`=(1 +2+1+2+1+2)/(7)=(9)/(7)=1.28571428571\approx1.29`

We can see that with outlier the mean is way higher than the mean of the rest of the values.

Hence, When an observation that is much larger than the rest of the data is added to a data set, the value of the mean will get affected.