Question

Consider the data set. 2, 3, 5, 6, 7

Answer 1

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