Question

1) Calculate the standard deviation and variance of the sample quantitative data shown, to two decimal places.

x
1.6
7.9
25.1
25.7
14.3

A) Standard deviation:  
B) Variance:  

2) In a neighborhood donut shop, one type of donut has 570 calories, seven types of donuts have 410 calories, four types of donuts have 360 calories, five types of donuts have 450 calories, and seven types of donuts have 600 calories.

A) Find the range.



B) Find the standard deviation. Round your answer to the nearest tenth, if necessary.

Answer 1

1)

a)

X	(X - X̄)²
1.6	177.42
7.9	49.28
25.1	103.63
26	116.21
14	0.38

	X	(X - X̄)²
total sum	74.6	446.93
n	5	5

                      
sample variance =    Σ(X - X̄)²/(n-1)=   446.9280   /   4   =   111.73
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (446.928/4)   =       10.57

2)

a)

maximum =    600              
minimum=   360              
                  
range=max-min =    600   -   360   =   240

b)

X	(X - X̄)²
570	9587.67
410	3854.34
410	3854.34
410	3854.34
410	3854.34
410	3854.34
410	3854.340
410	3854.340
360	12562.674
360	12562.674
360	12562.674
360	12562.674
450	487.674
450	487.674
450	487.674
450	487.674
450	487.674
600	16362.674
600	16362.674
600	16362.674
600	16362.674
600	16362.674
600	16362.674
600	16362.674

	X	(X - X̄)²
total sum	11330	203795.83
n	24	24

sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (203795.8333/23)   =       94.1

Thanks in advance!

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