Question

Sample medians List all $10$possible SRSs of size $\mathrm{n}=3$, calculate the median quiz score for each sample, and display the sampling distribution of the sample median on a dotplot.

Short answer

The median quiz score for each sample :

Sample size $3$	Median
Abigail - Bobby - Carlos	$(10,5,10)=10$
Abigail - Bobby - DeAnna	$(10,5,7)=7$
Abigail - Bobby - Emily	$(10,5,9)=9$
Abigail - Carlos - DeAnna	$(10,10,7)=10$
Abigail - Carlos - Emily	$(10,10,9)=10$
Abigail - DeAnna - Emily	$(10,7,9)=9$
Bobby - Carlos - DeAnna	$(5,10,7)=7$
Bobby - Carlos - Emily	$(5,10,9)=9$
Carlos - DeAnna - Emily	$(10,7,9)=9$

The dot plot :

Step-by-step solution

Given information

We need to find the median quiz score for each sample, and display the sampling distribution of the sample median on a dotplot for given table

Name	Gender	Quiz score
Abigail	Female	$10$
Bobby	Male	$5$
Carlos	Male	$10$
DeAnna	Female	$7$
Emily	Female	$9$

Simplify

Median can be calculated by arranging the data in ascending or descending order.

The median quiz score for each sample :

Sample size	Median
Abigail - Bobby - Carlos	$(10,5,10)=10$
Abigail - Bobby - DeAnna	$(10,5,7)=7$
Abigail - Bobby - Emily	$(10,5,9)=9$
Abigail - Carlos - DeAnna	$(10,10,7)=10$
Abigail - Carlos - Emily	$(10,10,9)=9$
Abigail - DeAnna - Emily	$(10,7,9)=9$
Bobby - Carlos - DeAnna	$(5,10,7)=7$
Bobby - Carlos - Emily	$(5,10,9)=9$
Bobby - DeAnna - Emily	$(5,7,9)=7$
Carlos - DeAnna - Emily	$(10,7,9)=9$

A dot plot is a graph that shows the distribution of numerical variables by using dots to represent values.
If a value appears more than once in a whole number, the dots are stacked one on top of the other, with the height of the column of dots representing the frequency of that value.