Question

Given the sample data.

x: Given the sample data.

x: 23, 17,15,32,25

(a)

Find the range. (Enter an exact number.)

(b)

Verify that Σx = 112 and Σx² = 2,692. (For each answer, enter an exact number.)
Σx =  
Σx² =  

(c)

Use the results of part (b) and appropriate computation formulas to compute the sample variance s² and sample standard deviation s. (For each answer, enter a number. Round your answers to two decimal places.)
s² =  
s =  

(d)

Use the defining formulas to compute the sample variance s² and sample standard deviation s. (For each answer, enter a number. Round your answers to two decimal places.)
s² =  
s =  

(e)

Suppose the given data comprise the entire population of all x values. Compute the population variance σ² and population standard deviation σ. (For each answer, enter a number. Round your answers to two decimal places.)
σ² =  

σ =

Answer 1

(a)

Range = Maximum - Minimum = 32 - 15 = 17

(b)

x	x2
23	529
17	289
15	225
32	1024
25	625
Total = 112	2692

Thus, we verify:

(c)

Sample Variance (s2) is given by:

Sample Standard Deviation (s) is given by:

(d)

Sample Mean () is given by:

x	x-	(x - )2
23	0.6	0.36
17	-5.4	29.16
15	-7.4	54.76
32	9.6	92.16
25	2.6	6.76
Total =		183.20

Sample Variance (s2) is given by:

Sample Standard Deviation (s) is given by:

(e)

Population Mean () is given by:

x	x-	(x - )2
23	0.6	0.36
17	-5.4	29.16
15	-7.4	54.76
32	9.6	92.16
25	2.6	6.76
Total =		183.20

Population Variance () isgiven by:

Population Standard Deviation () is given by: