Question

Identify the outlier in the data set, and determine how the outlier affects the mean, median, and mode of the data. Then tell which measure of central tendency best describes the data with and without the outlier. Justify your answer. 85, 91, 83, 78, 79, 64, 81, 97

Answer 1

Kindly check explanation

Explanation:

Given the data:

85, 91, 83, 78, 79, 64, 81, 97

Ordered data : 78, 79, 81, 83, 85, 91, 97

Mean:

Σx / n =

n = sample size = 8

(64+78+79+81+83+85+91+97) / 8

= 658 / 8

= 82.25

Median = 1/2(n+1)th term

1/2(8+1)th term = 1/2 * 9 = 4.5th term

(4th term + 5th term) /2 = (81 + 83) / 2 = 82

Mode = 85, 91, 83, 78, 79, 64, 81, 97

Outlier:

Lower = Q1 - 1.5(IQR)

Upper = Q3 + 1.5(IQR)

Using a calculator :

Q1 = 78.5 ; Q3 = 88 ;

IQR = (Q3 - Q1)

(88 - 78.5) = 9.5

Outlier :

78.5 - 1.5(9.5) = values < 64.25

88 + 1.5(9.5) = values > 102.5

Hence. Outlier is 64

Removing the Outlier :

Data = 78, 79, 81, 83, 85, 91, 97

Mean = 84.85

Median = 83

Based on the result, the median is the best measure of central tendency for the data: