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Consider the data set. 2, 3, 5, 6, 7
(a) Find the range.
(b) Use the defining formula to compute the sample standard deviation s. (Round your answer to two decimal places.)
(c) Use the defining formula to compute the population standard deviation σ. (Round your answer to two decimal places.)

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Answer:

5 ; 2.07 ; 1.85

Step-by-step explanation:

Given the data:

2, 3, 5, 6, 7

The range : ( highest - lowest)

The range = (7 - 2) = 5

Sample standard deviation :

sqrt[Σ(x - m)²/ (n - 1)]

The mean (m) = Σx / n

n = sample size = 5

Σx / n ;

(2+3+5+6+7) / 5

= 23 / 5

= 4.6

[(2-4.6)^2 + (3-4.6)^2 +(5-4.6)^2 + (6-4.6)^2+ (7-4.6)^2] / (5 - 1)

= 17.2 / 4

= 4.3

Sqrt(4.3) = 2.07

Population standard deviation :

sqrt[Σ(x - m)²/ n]

The mean = m = 4.6

n = sample size = 5

[(2-4.6)^2 + (3-4.6)^2 +(5-4.6)^2 + (6-4.6)^2+ (7-4.6)^2] / 5

= sqrt(17.2 / 5)

= sqrt(3.44)

= 1.8547 = 1.85

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