Central Tendency - Mean, Median, and Mode

This article explains the concept of central tendency and how to calculate mean, median, and mode. It also discusses the appropriateness of each measure in different types of distributions.

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Student’s name:
Professor’s name:
Course Name:
Date:
Central Tendency
Question 1
a)
The diagram below shows the stem plot of the pulse data. The stem has breaks of five for the
digits 01, 23, 45, 67, and 89.
5
.
.
. 6 6
.
6 0
. 2
. 4
.
. 8 8 8 8
7 0 0 0 0 0 0
. 2 2 2 2 2 2 2
. 4 4 4 4 4
. 6 6
. 8 8
b)
Mean is the calculated averages of a set of numbers (Speigel & Murray, p.3). Thus the
formula;

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= μ = (∑xi) / N
μ = (56 + 56 + 60 + 62 + 64 + 68 + 68 + 68 + 68 + 70 + 70 + 70 + 70 + 70 + 70 + 72 + 72 +
72 + 72 + 72 + 72 + 72 + 74 + 74 + 74 + 74 + 74 + 76 + 76 + 78 + 78) / 31
μ =70
Median is the middle value of a sorted list of numbers (Gott, Richard & Wesley, p. 1397).
Thus, the median is 72.
Mode is the set of data values that appears most often (Sullivan, p.18). Thus the mode is 72.
c)
It is evident from the figure in question (a) that the distribution is negatively skewed.
Thus, the median is the most preferred as a brief description of the centre of the distribution
in question (b) above. Moreover, based on this criterion, it can be claimed that the mode is
also appropriate. The mean is not appropriate since it is used in distributions that are not
skewed. The mean is used in data that is symmetrical and normally distributed.
Question 3
a)
Mean = μ = (∑xi)/N
μ = (42 + 47 + 49 + 58 + 43 + 47 + 44 + 38 + 38 + 28 + 55 + 40 + 46 + 54 + 45 + 45 + 51 +
35 + 46 + 37 + 46 + 40 + 43 + 49 + 37) / 25
μ = 44.12

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Median
Sorted data:
28 35 37 37 38 38 40 40 42 43 43 44 45
45 46 46 46 47 47 49 49 51 54 55 58
Median = 45
b)
c) The mean is the
most preferred as a brief description of the centre of the distribution in question (b) above.
From the stem plot on question (b), it can be seen that the distribution is normal and it is
symmetrical. Thus the mean is the most appropriate measures of central distribution.
The median is suitable in being used in distributions that are skewed, either positively or
negatively. Consequently, the mode can also be used in similarly to the median as long as the
distribution is skewed.
References:
1
2 8
3 5 7 7 8 8
4 0 0 2 3 3 4 5 5 6 6 6 6 7 9 9
5 1 4 5 8
6

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Gott III, J. Richard, and Wesley N. Colley. "Median statistics in polling." Mathematical and
Computer Modelling 48.9-10 (2008): 1396-1408.
Spiegel, Murray R., and Larry J. Stephens. Schaum's outline of statistics. McGraw Hill
Professional, 2017.
Sullivan III, Michael. Fundamentals of statistics. Pearson, 2015.