Question

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

Short answer

The minimum sampling :

Sample of size $3$	Sample Mean
Abigail - Bobby - Carlos	$5$
Abigail - Bobby - DeAnna	$5$
Abigail - Bobby - emily	$5$
Abigail - Carlos - DeAnna	$7$
Abigail - Carlos - Emily	$9$
Abigail - DeAnna - Emily	$7$
Bobby - Carlos - DeAnna	$5$
Bobby - Carlos - Emily	$5$
Bobby - DeAnna - Emily	$5$
Carlos - DeAnna - Emily	$7$

The dotplot is given below:

Step-by-step solution

Given information

We need to find minimum quiz score for each sample, and display the sampling distribution of the sample minimum 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

As we know sample mean is minimum of the quiz score of sample.

Now, $\mathrm{n}=3$, therefore,

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

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.

Now from the above table, dot plot will be :

From dot plot,

Centre is about $8.25$

Minimum $=6$

Maximum $=10$

Range $=4$

The distribution is slightly negative of left skewed.