Question

A data set yielded the following information:
The sample mean is 45.
The sample standard deviation is 17.1.

(a) According to the z-score criterion, how small does a value in this data set have to be in order to be called an outlier from below?

(b) According to the z-score criterion, how large does a value have to be in order to be called an outlier from above?

Answer 1

a)

Answer:

The data value = -6.3

Explanation:

According to the z score criteria, a data point is considered an outlier if it lies 3 standard deviations below the mean such that if the z score is less than -3.

Given:

Let the data point x is the outlier, then using the z score formula

hence a data point will be considered an outlier if its value is less than -6.3.

b)

Answer:

The data value = 96.3

Explanation:

According to the z score criteria, a data point is considered an outlier if it lies 3 standard deviations above the mean such that if the z score is greater than 3.

Let the data point x is the outlier, then using the z score formula

hence a data point will be considered an outlier if its value is greater than 96.3.