Question

In an examination given to a class of 20 students, the following test scores were obtained.

45 45 50 50 55 60 70 75 75 80
80 85 85 85 85 90 95 95 95 100
a) Find the mean (or average) score, the mode, and the median score.
b) Which of these three measures of central tendency do you think is the least representative of the set of scores?

Answer 1

Mean = 75

Median = 80

Mode = 85

The mode

Explanation:

Given the data :

45 45 50 50 55 60 70 75 75 80 80 85 85 85 85 90 95 95 95 100

Rearranged data :

45, 45, 50, 50, 55, 60, 70, 75, 75, 80, 80, 85, 85, 85, 85, 90, 95, 95, 95, 100

The mean score :

ΣX / n ; n = sample size = 20

ΣX = 1500

Mean = 1500 / 20 = 75

Mode = most frequently occurring = 85 ( frequency of 4)

Median = 0.5(n + 1)th term

Median = 0.5(20 + 1)th term

Median = 0.5(21) th term

Median = 10.5th term = (10 + 11)th term / 2

Median = (80 + 80) / 2 = 160 / 2 = 80

2.) The mode