Question

Outliers existing in a data set will have the greatest impact on __________. A. the mean B. the median C. the mode D. the middle

Answer 1

Outliers existing in a data set will have the greatest impact on :

option: A is the correct answer.

A. The mean.

Step- by- step explanation:

We know that an outlier is a data value or the data point that stands out of the rest of the data points of the set i.e. it either attains a too high or too low value as compared to other data points.

Hence, the outlier will effect the mean of the data set.

( Since, when a too low value is present in the set then after removing that value the mean of remaining elements or data points will increase after removing the outlier.

For example if we have data set as:

1 30 34 39 41 45

Then mean of the set is:

`Mean=(1+30+34+39+41+45)/(6)\\\\\\Mean=31.667`

and on removing 1 from the set we get:

`Mean=(30+34+39+41+45)/(5)\\\\\\Mean=37.8`

Hence, we see that the mean is increased.

Similarly, if there is a data value which is too high then after removing that element the mean of the remaining data points will decrease )

Answer 2

Outliers are the ones that are least precise among the data. They may be due to experimental or human errors. In the case of having outlier in the data, its effect is most significant n computing the mean because they are included in the calculation. The median mode and middle do not involve calculation but only the ordination, so they are not affected.