Question

Consider the data set.

• 2,
• 3,
• 4,
• 6,
• 8

(a)

Find the range. (Enter an exact number.)

(b)

Use the defining formula to compute the sample standard deviation s. (Enter a number. Round your answer to two decimal places.)

(c)

Use the defining formula to compute the population standard deviation σ. (Enter a number. Round your answer to two decimal places.)

Answer 1

Solution :

(a)

Maximum = 8

Minimum = 2

Range = maximum - minimum = 8 - 2 = 6

n = 5

(b)

= = (2 + 3 + 4 + 6 + 8) / 5 = 23 / 5 = 4.6

s =  (x - )² / n - 1  

= (2 - 4.6)² + (3 - 4.6)² + (4 - 4.6)²​​​​​​​ + (6 - 4.6)²​​​​​​​ + (8 - 4.6)²​​​​​​​ / 5 - 1

= 23.2 / 4

= 5.8

= 2.41

(c)

= = (2 + 3 + 4 + 6 + 8) / 5 =

= (x - )² / n

= (2 - 4.6)² + (3 - 4.6)²​​​​​​​ + (4 - 4.6)²​​​​​​​ + (6 - 4.6)²​​​​​​​ + (8 - 4.6)²​​​​​​​ / 5

= 23.2 / 5

= 4.64

= 2.15