Question

Nine people standing in an elevator are the following ages:

5, 15, 25, 30, 35, 40, 45, 55, 65

What is the total number of data points (n) in the given set of data?

What is the mean age (μ) of the people in the elevator?

Complete the following table:

xx	(x−μ)x−μ	(x−μ)2x−μ2
5
15
25
30
35
40
45
55
65
	Total = Σ(x−μ)2x−μ2 =

Given the correct value for Σ(x−μ)2x−μ2 and the value for n, what is the variance (σ2σ2) of the given set of data (written to two decimal places without rounding)?

Variance = σ2σ2 =

Using the correct value for the variance as calculated (written to two decimal places with no rounding), what is the standard deviation (σ) of the given set of data (also written to two decimal places with no rounding)?

Standard deviation = σ =

Answer 1

(a)

Total number of data points =n = 9

(b)

Mean () is given by:

So,

Mean = = 35

(c)

x	(x - )	(x - )2
5	- 30	900
15	- 20	400
25	- 10	100
30	- 5	25
35	0	0
40	5	25
45	10	100
55	20	400
65	30	900
Total =		2850

(d)

Variance () is got as follows:

So,

Variance = 316.67

(e)

Standard Deviation () is given by:

So,

StandardDeviation = 17.80