Central Tendency - Mean, Median, and Mode

Surname 1
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;

Surname 2
= 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