Q. 3.207 - Elementary Statistics

Question

Age of U.S. Residents. The U.S. Census Bureau collects information about the ages of people in the United States. Results are published in Current Population Reports

a. Identify the variable and population under consideration.

b. A sample of six U.S. residents yielded the following data on ages (in years). Determine the median of these age data. Decide whether this descriptive measure is a parameter or a statistic, and use statistical notation to express the result.

c. By consulting the most recent census data, we found that the median age of all US residents is $37.2 yrs$. Decide whether that descriptive measure is a parameter or a statistic and use statistical notation to express the result

Step-by-Step Solution

Answer

(a) The variable under consideration is age and the population under consideration is All people in the United States

(b) The median is, $M=37 years$, and descriptive measure is statistics.

(c) Descriptive measure is parameter and its statistical notation is, $\eta =37.2$

Part (a) Step 1: Given information

We need to find out the variable and population under consideration

Part (a) Step 2: Explanation

Age is the variable under consideration and All people of the United States are the population under consideration.

Part (b) Step 1: Given information

We are given that, 

The data set in ordered list  is, 

   $7, 9, 29, 45, 51, 54$

Part (b) Step 2: Simplify

As we know that median is the middle value of sorted data.

So, the median is,

   $M=\frac{29+45}{2}=37$

Since the value of median depends upon given data.

Hence the value of median is statistic

Part (c) Step 1: Given information

We are given that, 

The median of data is, $M=37.2 yrs$

Part (c) Step 2: Explanation

As, The value of median depends upon all individuals in the population.

So, it is a parameter.

The population median is represented by $\eta$.

    $\eta =37.2$