Question

Problem 4. InfoMart Report

InfoMart is a research firm that collects and analyzes information for business firms, government agencies, non-profit organizations, and consumer clients. InfoMart has just completed a report comparing the demographic features of two cities that have similar size populations. In this question, you will examine some of the summary statistics that InfoMart computed with respect to two demographic variables: monthly household income, and age of the homeowner. These summary statistics are presented in the table below. (Homeowner age for Mountainview is not shown in the table, as it is not required to complete this problem.)

Computed Statistic	Mountainview: Household inc.	Rivercity: Household inc.	Rivercity: Homeowner age
Mean	4,300	4,300	45
Minimum	0	0	20
Maximum	10,200	10,200	70
First Quartile (Q1)	1,500	4,000	25
Second Quartile (Q2)	2,000	4,500	50
Third Quartile (Q3)	8,000	4,800	55
Standard Deviation	3,750	100	20

Figure 1. InfoMart data.

1. Determine the median monthly household income for each city as shown in the table above. [2 marks]
2. In Rivercity, which variable, income or age, exhibits the greater degree of relative variability? Compute the appropriate statistics. [4 marks]
3. In Mountainview, within what range of monthly household income does the middle 50% of households fall? [2 marks]

Answer 1

a)

Mean = (Minimum + 2 * Median + Maximum)/4

So,

Median = (4 Mean – Minimum – Maximum)/2

For Mountainview,

Median = (4*4300-0-10200)/2 = 3500

For Rivercity,

Median = (4*4300-0-10200)/2 = 3500

b)

Measures of Variability are Range, Interquartile Range, Variance and Std Deviation

Where Range = Maximum – Minimum

Interquartile Range = Third Quartile – First Quartile.

So,

The most commonly use statistic is Range.

Since the value of Household income is much larger than Homeowner Age, hence it has more degree of variability.

c)

Middle 50% is the value of Interquartile Range ie IQR

Hence, for Mountainview

IQR = Q3 – Q1 = 8000 – 1500 = 6500