Question

Remove the largest number from each data set and repeat the calculations (samplecomparison.xlsx). Answer the questions below.

The range of the first data set is _____ .

The variance of the first data set is _____ . (Round to three decimal places as needed)

The standard deviation of the first data set is _____ . (Round to three decimal places as needed)

The range of the second data set is _____ .

The variance of the second data set is _____ . (Round to three decimal places as needed)

The standard deviation of the second data set is _____ . (Round to three decimal places as needed)

Sample Comparison Data:

Sample 1	Sample 2
11	23
9	36
6	25
14	33
27	35
28	40
19	21
21	38
23	35
129	34

Answer 1

Sample 1

	x	x-x̅	(x-x̅)2
	11	-17.7	313.29
	9	-19.7	388.09
	6	-22.7	515.29
	14	-14.7	216.09
	27	-1.7	2.89
	28	-0.7	0.49
	19	-9.7	94.09
	21	-7.7	59.29
	23	-5.7	32.49
	129	100.3	10060.09
Total	Σx = 287		Σ(x-x̅)2 = 11682.1

x̅ = Σx/n = 287/10 = 28.700

Σ(x-x̅)² = 11682.100

Sample variance = (Σ(x-x̅)²)/(n-1) = 11682.1/9 = 1298.011

Sample standard deviation = 1298.011^0.5 = 36.028

Range = Maximum-Minimum = 129-6 = 123

Sample 2

	x	x-x̅	(x-x̅)2
	23	-9	81.00
	36	4	16.00
	25	-7	49.00
	33	1	1.00
	35	3	9.00
	40	8	64.00
	21	-11	121.00
	38	6	36.00
	35	3	9.00
	34	2	4.00
Total	320		390.000

x̅ = Σx/n = 320/10 = 32.000

Σ(x-x̅)² = 390.000

Sample variance = (Σ(x-x̅)²)/(n-1) = 390/9 = 43.333

Sample standard deviation = 43.333^0.5 = 6.583

Range = Maximum-Minimum = 40-21 = 19