True or False? The population standard deviation and sample standard deviation are of the same value if the population and sample size are the same.

reinzogoq

reinzogoq

Answered question

2022-09-03

True or False? The population standard deviation and sample standard deviation are of the same value if the population and sample size are the same.

Answer & Explanation

Gracelyn Paul

Gracelyn Paul

Beginner2022-09-04Added 17 answers

The population standard deviation formula is,
σ = ( X μ ) N
Where μ be the population mean, and N be the population size.
The sample standard deviation formula is,
σ = ( X x ¯ ) n 1
Where x ¯ be the population mean, and n be the sample size.
Even though the size of population and sample are same, both are completely as the population is all the individuals in the study whereas subset of population is sample. The standard deviation of population is calculated based on population mean and the standard deviation of sample is calculated from sample mean. The standard deviation of population would be different from sample. This implies that, the given statement is false.
Correct Answer: False.

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