Question

Refer to the small population of $5$students in the table.

Sample means List all $10$ possible SRSs of size $n=2$, calculate the

mean quiz score for each sample, and display the sampling distribution of the sample

mean on a dotplot.

Short answer

Answer to the given question:

Sample of size$2$	Sample mean
Abigail-Bobby	$7.5$
Abigail-Carlos	$10$
Abigail-DeAnna	$8.5$
Abigail-Emily	$9.5$
Bobby-Carlos	$7.5$
Bobby-DeAnna	$6$
Bobby-Emily	$7$
Carlos-DeAnna	$8.5$
Carlos-Emily	$9.5$
DeAnna-Emily	$8$

Dotplot:

Step-by-step solution

Given information

Sample of size $2$	Gender	Quiz score
Abigail	Male	10
Bobby	Female	5
Carlos	Female	10
DeAnna	Male	7
Emily	Male	9

Explanation

All the possible samples of size $2$then contain any two (different) people of the population of $5$students.

Sample of size$2$

Abigail-Bobby

Abigail-Carlos

Abigail-DeAnna

Abigail-Emily

Bobby-Carlos

Bobby-DeAnna

Bobby-Emily

Carlos-DeAnna

Carlos-Emily

DeAnna-Emily

The sample mean of a sample is then the sum of the two corresponding quiz scores divided by the number of data values.

Sample of size$2$	Sample mean
Abigail-Bobby	$\overline{x}=\frac{10+5}{2}=\frac{15}{2}=7.5$
Abigail-Carlos	$\overline{x}=\frac{10+10}{2}=\frac{20}{2}=10$
Abigail-DeAnna	$\overline{x}=\frac{10+7}{2}=\frac{17}{2}=8.5$
Abigail-Emily	$\overline{x}=\frac{10+9}{2}=\frac{19}{2}=9.5$
Bobby-Carlos	$\overline{x}=\frac{5+10}{2}=\frac{15}{2}=7.5$
Bobby-DeAnna	$\overline{x}=\frac{5+7}{2}=\frac{12}{2}=6$
Bobby-Emily	$\overline{x}=\frac{5+9}{2}=\frac{14}{2}=7$
Carlos-DeAnna	$\overline{x}=\frac{10+7}{2}=\frac{17}{2}=8.5$
Carlos-Emily	$\overline{x}=\frac{10+9}{2}=\frac{19}{2}=9.5$
DeAnna-Emily	$\overline{x}=\frac{7+9}{2}=\frac{16}{2}=8$

Dotplot:

Create a number line

For every given data value place a dot above the corresponding number on the number line.