Question

Given the sample data. x: 21 17 15 32 25

(a) Find the range.

(b) Verify that Σx = 110 and Σx2 = 2,604.

Σx =

Σx2 =

(c) Use the results of part (b) and appropriate computation formulas to compute the sample variance s2 and sample standard deviation s. (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. (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. (Round your answers to two decimal places.)

σ2 =

σ =

Answer 1

Given sample of 5 data values are : 21, 17, 15, 32, 25

a) Minimum value = 15 and Maximum value = 32

Range = Maximum value - Minimum value = 32 - 15 = 17

=> Range = 32

b) Σx = 21 + 17 + 15 + 32 + 25 = 110

=> Σx = 110

Σx^{​​​​​2}= (21)² + (17)² + (15)² + (32)² + (25)² = 2604

Σx^{​​​​​2} = 2604

c) Sample variance is,

sample standard deviation is,

=> S^{​​​​​​2} = 46

=> S = 6.78

d) Population variance is,

Population standard deviation is,

=> σ^{​​​​​​2} = 36.80

=> σ = 6.07