Question

Which of the following statistics are unaffected by a single large outlier? (More than one)
a. Median
b. Interquartile range
c. Variance
d. Range
e. Mean
f. Mode

Answer 1

The following statistics are unaffected by a single large outlier in a dataset:

Median, Interquartile Range, Mode

The reason for that is:-

Median- It is the middle value in the dataset when it's values are arranged in ascending or descending order. So the presence of an outlier does not affect the ascending or descending order of the values in the dataset and hence the median is unaffected.

Interquartile Range- It is the difference between the 3rd quartile & 1st quartile.1st quartile & 3rd quartile are the values below which the 1/ 4th & 3/4th of the total number of values in a dataset arranged in an ascending order lies respectively. Just like the median,  the presence of an outlier does not affect the ascending order and hence their difference i.e the Interquartile Range remains unaffected.

Variance- It is the sum of the squared distances of each value in the dataset from it's mean. So the presence of outlier results in the increase of variance as the distance from the outlier from mean is greater than that of the other values in the dataset. So, the variance is significantly affected by outliers.

Range- It is the difference between the maximum & minimum value in a dataset. So, the presence of outliers changes the maximum & minimum values and hence affects the range significantly.

Mean- It is the average of all the values in a dataset. So, a presence of an outlier i.e an extreme value significantly affects its value.

Mode- It is the value of the dataset which has the highest frequency, i.e which value is repeated the maximum number of times in the dataset. Since outlier consists of few observations, it does not affect the value of the dataset which has the highest frequency i.e mode.