Question

Calculate the population mean and median based on the numerical values of Satisfaction Level, and then interpret those at the nominal level.

TABLE C6-2: Customer Satisfaction
Customer Number	Customer Name			Satisfaction Level	Level No.
1	Anderson			Very high	4
7	Hetfield			very high	4
14	Luo			very high	4
15	Madras			very high	4
19	Nickens			very high	4
20	Poteau			very high	4
2	Angero			high	3
5	Chontos			high	3
9	Jamesson			high	3
11	Lehmann			high	3
12	Lee			high	3
22	Scully			high	3
23	Singh			high	3
24	Skinner			high	3
27	Vu'oto			high	3
29	Yap			high	3
3	Ball			medium	2
8	Iruja			medium	2
10	Kemp			medium	2
17	Mulder			medium	2
21	Sakomoto			medium	2
26	Tang			medium	2
28	Walker			medium	2
4	Bobak			low	1
13	Lewins			low	1
16	Morris			low	1
18	Ngozichi			low	1
25	Suzuki			low	1
6	Detley			very low	0
30	Zindermanelino			very low	0
Very High		4
High		3
Medium		2
Low		1
Very Low		0

Answer 1

The mean (or average) is the most popular and well-known measure of central tendency. It can be used with both discrete and continuous data, although its use is most often with continuous data. The mean is equal to the sum of all the values in the data set divided by the number of values in the dataset.

The median is the middle score for a set of data that has been arranged in order of magnitude. The median is less affected by outliers and skewed data.

we have 30 data points so our median will sum of 15th and 16th value divided by 2

median = (3+3)/2 = 3

So from above two measures of central tendency, we have mean of 2 and median of 3.

So the satisfaction level has the mean value of medium and median of High. if we plot histogram of the levels we get

we can see our data is roughly normal and the data is skewed towards the right that is why we have different values of mean and median. Also in case of skewed data, we should consider median as the measure of central tendency.