Question

Perform each task, given the following set of data. 3 6 11 13 19 23 (a) Viewing the data as a sample drawn from a larger population, find the sample standard deviation, s, of the data. (Round your answer to two decimal places.) s = (b) Viewing the data as an entire population, find the population standard deviation, σ, of the data. (Round your answer to two decimal places.) σ = (c) How do the answers to parts (a) and (b) compare? Why? The sample standard deviation is greater. The standard deviation formulas have the same numerator, but the sample standard deviation has a larger denominator, and thus is the greater quantity. The sample standard deviation and population standard deviation are equal. The population standard deviation has a larger denominator, but the sample standard deviation has a larger numerator, and thus both work out to the same quantity. The population standard deviation is greater. The standard deviation formulas have the same numerator, but the population standard deviation has a larger denominator, and thus is the greater quantity. The population standard deviation is greater. The standard deviation formulas have the same numerator, but the population standard deviation has a smaller denominator, and thus is the greater quantity. The sample standard deviation is greater. The standard deviation formulas have the same numerator, but the sample standard deviation has a smaller denominator, and thus is the greater quantity.

Answer 1

a.

Given Data

x_i : 3,6,11,13,19,23

Sample standard deviation formula

n : Number of observations=6

s=7.58

b.

Population standard deviation formula

c.

How do the answers to parts (a) and (b) compare? Why?

The sample standard deviation is greater

The standard deviation formulas have the same numerator, but the sample standard deviation has a smaller denominator, and thus is the greater quantity.

As can be observed ;

s: sample standard deviation : 7.58 > population standard deviation : :6.92;

Also Numerator is same for both of them : i.e .

Denominator for sample standard deviation :   is smaller than denominator for population standard denominator : ;

Hence larger quantity for sample standard deviation : s