Question

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

(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

ANSWER:

Given data,

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

(a) Find the range. (Enter an exact number.)

In order {2, 3, 5, 6, 7}

the lowest value is 2, and

the highest is 7.

the range = highest - lowest = 7- 2 = 5

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

Mean = $\bar{x}$ = (2+3+5+6+7)/5 = 23/5 = 4.6

Sample standard deviation = s = sqrt((x-$\bar{x}$)^2/(n-1))

= sqrt((2-4.6)^2+(3-4.6)^2+(5-4.6)^2+(6-4.6)^2+(7-4.6)^2 / (5-1))

= sqrt(17.2 /4)

= 2.07364

s = 2.07 (Rounded 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.)

population standard deviation = σ = sqrt((x-$\bar{x}$)^2/(n))

= sqrt((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)

= 1.85472

σ = 1.85 (Rounded two decimal places)

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