Question

The weekly total of hours for the servers and the cooks for a small restaurant are listed below. Find the range, variance, and standard deviation for each set. Which set of data is more variable? (75–150 words, or 1–2 paragraphs)

Week 1 2 3 4 5 6 7 8 9 10 Servers 823 837 858 791 812 814 832 862 833 826 Cooks 752 764 754 774 771 745 736 816 792 793

Answer 1

The given data is as follows:

week	servers	cooks
1	823	752
2	837	764
3	858	754
4	791	774
5	812	771
6	814	745
7	832	736
8	862	816
9	833	792
10	826	793

This can be solved using excel<data<megastat<descriptive statistics

The output is as follows:

Descriptive statistics
	servers	cooks
count	10	10
mean	828.80	769.70
sample standard deviation	21.14	24.82
sample variance	446.84	615.79
minimum	791	736
maximum	862	816
range	71	80

	Formulas	Servers	Cooks
Range	Maximum Value-Minimum value	862-791=71	816-736=80
Mean (x)
Standard Deviation
Variance		446.84	615.79
Coefficient of variation		2.55052	3.224

The range, variance, and standard deviation for Servers are 71,446.84,21.14.

The range, variance, and standard deviation for cooks are 80,615.79,24.82.

Now we have to check which data set is more variable. As to check which data is more variable, we can use the coefficient of variation of observations to describe the level of variability between two sets. The higher the level of coefficient of variation means there is high variability in that set.

Since the coefficient of variation of Cooks is greater than the Servers. This means that the data set cooks are more variable than the data set servers.

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