Question

Given the sample data.

x:

• 21,
• 19,
• 13,
• 32,
• 27

(a)

Find the range. (Enter an exact number.)

(b)

Verify that Σx = 112 and Σx² = 2,724. (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

Solution:

The sample data.

x:

• 21,
• 19,
• 13,
• 32,
• 27

Part a) Find the range.

Range = Max - Min

Range = 32 - 13

Range = 19

Part b) Verify that Σx = 112 and Σx² = 2,724.

x	x^2
21	441
19	361
13	169
32	1024
27	729

Thus

Part c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s² and sample standard deviation s.

and

Part d) Use the defining formulas to compute the sample variance s² and sample standard deviation s.

Thus we need to make following table:

x	(x-xbar)	(x-xbar)^2
21	-1.4	1.96
19	-3.4	11.56
13	-9.4	88.36
32	9.6	92.16
27	4.6	21.16

Thus

and

Part e) Suppose the given data comprise the entire population of all x values. Compute the population variance σ² and population standard deviation σ.

and