Measures of Central Tendency

Calculate and label the sample sum, n, mode, median, and mean (show your work)

Data set #1: 27, 65, 61, 15, 71, 41, 11, 2, 7, 15, 39, 16, 27, 39, 10

Sum

Sum, 27 + 65 + 61 + 15 + 71 + 41 + 11 + 2 + 7 + 15 + 39 + 16 + 27 + 39 + 10

= 446

Sample size, n

The sample size, n

There are fifteen samples, thus, n = 15

Mode

The mode is a measure of central tendency referring to data value with the highest frequency.

27, 65, 61, 15, 71, 41, 11, 2, 7, 15, 39, 16, 27, 39, 10

Step I: Arranging the data set in ascending order

2, 7, 10, 11, 15, 15, 16, 27, 27, 39, 39, 41, 61, 65, 71

Step II: Identifying the most recurring value(s)

Value Frequency
2 1
7 1
10 1
11 1
15 2
16 1
27 2
39 2
41 1
61 1
65 1
71 1

 

The values with the highest frequency are 15, 27 and 39 with each occurring twice. Therefore, the Mode of the data set is 15, 27, and 39.

This phenomenon, where there are three modes in a data set, is known as trimodal.

Median

Median is a measure of central tendency referring to the center-most data value.

27, 65, 61, 15, 71, 41, 11, 2, 7, 15, 39, 16, 27, 39, 10

Step I: Arranging the data set in ascending order

2, 7, 10, 11, 15, 15, 16, 27, 27, 39, 39, 41, 61, 65, 71

Step II: Identifying the center-most value

In the data set 2, 7, 10, 11, 15, 15, 16, 27

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