Q. 3.192 - Elementary Statistics

Question

Identify each quantity as a parameter or a statistic

(a) $\mu$          (b)$s$           (c)$\overline{x}$            (d)$\sigma$

Step-by-Step Solution

Answer

(a) $\mu$ is parameter quantity.

(b) $s$ is statistic quantity.

(c) $\overline{x}$ is statistic quantity.

(d) $\sigma$ is parameter quantity.

Part(a) Step 1: Given Information

We are given  quantity $\mu$ 

We need to identify whether quantity is parameter or statistic

Part(a) Step 2: Explanation

A parameter is a number that describes the entire population characteristics .

A statistic is a number that describes characteristics of a sample.

Greek and capital letters typically refer to populations, but Latin and lower-case letters usually refer to samples.

From above definitions we can elaborate that

$\mu$ is parameter quantity.

Part(b) Step 1: Given Information

We are given  quantity $s$ 

We need to identify whether quantity is parameter or statistic

Part(b) Step 2: Explanation

A statistic is a number that describes characteristics of a sample.

Greek and capital letters typically refer to populations, but Latin and lower-case letters usually refer to samples.

From above definitions we can elaborate that

$s$ is a statistic quantity.

Part(c) Step 1: Given Information

We are given  quantity $\overline{x}$ 

We need to identify whether quantity is parameter or statistic

Part(c) Step 2: Explanation

A statistic is a number that describes characteristics of a sample.

Greek and capital letters typically refer to populations, but Latin and lower-case letters usually refer to samples.

From above definitions we can elaborate that

$\overline{x}$is a statistic quantity.

Part(d) Step 1: Given Information

We are given  quantity $\sigma$ 

We need to identify whether quantity is parameter or statistic

Part(d) Step 2: Explanation

A parameter is a number that describes the entire population characteristics .

A statistic is a number that describes characteristics of a sample.

Greek and capital letters typically refer to populations, but Latin and lower-case letters usually refer to samples.

From above definitions we can elaborate that

$\sigma$ is a parameter quantity.