We have been given a table of quiz scores whose standard deviation is 5.6. We are asked to find the test scores that are within one standard deviation of the mean.
First of all, we will find the mean of the test scores using average formula.
[tex]\text{Average}=\frac{\text{Sum of data points}}{\text{Number of data points}}[/tex]
[tex]\text{Average}=\frac{25+13+16+30+27+22+19+22+15+28+27+29}{12}[/tex]
[tex]\text{Average}=\frac{273}{12}[/tex]
[tex]\text{Average}=22.75[/tex]
The scores within one standard deviation would be mean plus one SD and mean minus one SD that is:
[tex]22.75-5.6\text{ and } 22.75+5.6[/tex]
[tex]17.15\text{ and } 28.35[/tex]
Therefore, the quiz scores 17.15 and 28.35 are within one standard deviation of the mean.
