Question

Consider the data set given in the following scenario and complete the following steps. Indicate your answers by typing numeric responses in the spaces provided. Indicate negative numbers by typing a hyphen before the numerals. Write your answers out to two decimal places without rounding to obtain the answers for variance and standard deviation.

1.	Indicate the value for n, which is the total number of data points.
2.	Indicate the value for μ, which is the mean of the set of data.
3.	Complete the table computing the values for (x−μ)x−μ and (x−μ)2x−μ2 for each value in the given data set, and indicate the summation of these individual values.
4.	Compute the value for the variance, written out to two decimal places without rounding. Indicate your answer in the space indicated.
5.	Use the entered value for the variance to compute the value for the standard deviation. Use your answer for the variance (two decimal places without rounding) as the input for your computation of the standard deviation. Likewise, indicate your answer in the space indicated, written out to two decimal places without rounding.

Nine people standing in an elevator are the following ages:

22, 28, 46, 51, 59, 67, 72, 90, 96

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
8
16
17
23
29
35
41
42
50
	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 =

Answer 1

A) Given data

1) Nine people standing in an elevator are the following ages:

22, 28, 46, 51, 59, 67, 72, 90, 96

a) Total number of data points in given data (n) is

Data points (n) =9

b) Mean age

Mean =sum of total ages/number of observations

=(22+28+46+51+59+67+72+90+96)/9

=531/9 =59.

2nd problem:

2)Given data set

8, 16, 17, 23, 29, 35, 41, 42, 50

Total number of observations(n) =9

a) Mean (μ) =Total sum/n

=(8+16+17+23+29+35+41+42+50)/9

=261/9=29

b) Variance of the given data set

Variance =(X-μ) ² /(n-1)

(X-μ) ²=(8-29)^2 +(16-29)^2 +(17-29)^2 +(23-29)^2+(29- 29)^2 +(35-29)^2+(41-29)^2 +(42-29)^2 +(50-29)^2

=441+169+ 144+36+0+36+144+169+441

=1580

Therefore variance =1580/(9-1)

=1580/8 =197.5

b)standard deviation =sqrt(variance)

=(197. 5)^0.5 =14.053