Question

Calculating the mean, median, and mode when scores are changed or removed

Consider the following sample set of scores. Assume these scores are from a discrete distribution.
15 25 42 42 45 48 49 56 74 100

Answer 1

To calculate the mean, median, and mode, find the sum and divide by the total number of scores for the mean, arrange the scores in ascending order and find the middle value(s) for the median, and count the frequency of each value to find the mode. Hence mean=49.6, median= 45, mode=42.

Step-by-step explanation:

The mean is calculated by summing all the scores and dividing by the total number of scores. For the given sample set, the mean is calculated as follows:

mean= 496/10

= 49.6
The median is the middle value when the scores are arranged in ascending order. If there is an even number of scores, the median is the average of the two middle values. For the given sample set, the median is calculated as follows:

1. Arrange the scores in ascending order: 15, 25, 42, 42, 45, 48, 49, 56, 74, 100
2. The median is the middle value(s): 45

The mode is the value(s) that appears most frequently in the sample set. For the given sample set, the mode is calculated as follows:

• Each value is counted: 15: 1, 25: 1, 42: 2, 45: 1, 48: 1, 49: 1, 56: 1, 74: 1, 100: 1
• The most frequent value(s) is the mode: 42