Q. 3.192E - Elementary Statistics

Question

Identify each quantity as a parameter or a statistic: 

a. \(\mu \)

b. \(s\)

c. \(\bar{x}\)

d. \(\sigma \)

Step-by-Step Solution

Answer

Part a. The quantity \(\mu \)  is the mean of the population. It is the descriptive measure of the population, so the given quantity is a parameter.

Part b. The quantity \(s\)   is the sample standard deviation. It is the descriptive measure of the sample, so the given quantity is a statistic.

Part c. The quantity  \(\bar{x}\) is the sample mean. It is the descriptive measure of the sample, so the given quantity is a statistic.

Part d. The quantity \(\sigma \) is the standard deviation of the population. It is the descriptive measure of the population, so the given quantity is a parameter.

Part a. Step 1. Given information

The given quantity is \(\mu\)

Part a. Step 2. Explanation

The quantity \(\mu \)  is the mean of the population. It is the descriptive measure of the population, so the given quantity is a parameter. 

Part b. Step 1. Explanation

The quantity \(s\)   is the sample standard deviation. It is the descriptive measure of the sample, so the given quantity is a statistic. 

Part c. Step 1. Explanation

The quantity  \(\bar{x}\) is the sample mean. It is the descriptive measure of the sample, so the given quantity is a statistic. 

Part d. Step 1. Explanation

The quantity \(\sigma \) is the standard deviation of the population. It is the descriptive measure of the population, so the given quantity is a parameter.