Question

Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results.

Listed below are the measured radiation absorption rates​ (in W/kg) corresponding to various cell phone models. If one of each model is measured for radiation and the results are used to find the measures of​ variation, are the results typical of the population of cell phones that are in​ use?

1.331.33

1.031.03

1.071.07

0.770.77

1.051.05

0.720.72

1.191.19

1.291.29

0.560.56

The range of the sample data is

Upper W divided by kg.W/kg.

left parenthesis Upper W divided by kg right parenthesis squared .(W/kg)2.

kg.kg.

W.W.

Upper W divided by kg.W/kg.

​(Round to three decimal places as​ needed.)

Sample standard

deviationequals=nothing

▼

kg.kg.

Upper W divided by kg.W/kg.

left parenthesis Upper W divided by kg right parenthesis squared .(W/kg)2.

W.W.

​(Round to three decimal places as​ needed.)

Sample

varianceequals=nothing

▼

left parenthesis Upper W divided by kg right parenthesis squared .(W/kg)2.

W.W.

kg.kg.

Upper W divided by kg.W/kg.

​(Round to three decimal places as​ needed.)

If one of each model is measured for radiation and the results are used to find the measures of​ variation, are the results typical of the population of cell phones that are in​ use?

A.

​No, because it is necessary to have at least 5 of each cell phone in order to get a meaningful result. Only including one of each cell phone model is not representative of each cell phone model.

B.

​Yes, because the results from any sample of cell phones will be typical of the population.

C.

​Yes, because each model is being represented in the sample. Any sample that considers all possible cell phone models will produce results typical of the population of cell phones.

D.

​No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighted according to their size in the population.

Answer 1

(1)

Range = Maximum - Minimum

           = 1.33 - 0.56

           = 0.77

The range of the sample data is 0.77 W/Kg

(2)

From the given data, the following statistics are calculated:

n = 9

- 9.01/9 = 1.001

x	(x - )	(x - )2
1.33	0.3289	0.1082
1.03	0.0289	0.0008
1.07	0.0689	0.0047
0.77	- 0.2311	0.0534
1.05	0.0489	0.0023
0.72	- 0.2811	0.0790
1.19	0.1889	0.0357
1.29	0.2889	0.0835
0.56	- 0.4411	0.1946
Total =		0.5623

Sample Standard Deviation (s) is given by:

Sample Standard Deviation = 0.265 W/Kg

(3)

Sample Variance (s²) is given by:

So,

Sample Variance = 0.070 W²/Kg²

(4)

Correct option:

C.

​Yes, because each model is being represented in the sample. Any sample that considers all possible cell phone models will produce results typical of the population of cell phones.