Question

4) Briefly explain and give an example for each of the three measures of central tendency (mean, mode, and median) and each of the two measures of dispersion (range and standard deviation). (10 points)

Answer 1

There are three main measures of central tendencies such as mean, mode, and median. We know that the mean or arithmetic mean is defined as the summation of all values divided by the total number of values or observations. In general, mean is used in most of the situations. The mode is the observation of the data which is most repeated. The mode of the data is defined as the observation with highest frequency. The use of mode is some situations are important where it is not good to use mean. The median is the middle most value of the data when data observations are arranged in increasing or decreasing order.

The range is defined as the difference between the maximum observation of the data and minimum observation of the data. The standard deviation is the standard value used for measuring deviation within the observations.

Let us see example:

No.	Data
1	2
2	3
3	4
4	5
5	5
6	6
7	7
Total	32

Mean = 32/7 = 4.571429

Mode = 5

Median = 5

Minimum = 2

Maximum = 7

Range = 7 – 2 = 5

Standard deviation = sqrt[∑(X – mean)^2/(n – 1)] = 1.718249