Question

Three students were applying to the same graduate school. They came from schools with different grading systems. Which student had the best GPA when compared to other students at his school? Explain how you determined your answer.

Short answer

Kamala had the highest GPA of the three students since her z-score was the highest.

Step-by-step solution

To determine

When compared to other students at his school, which student achieved the highest GPA.

Explanation

The mean is one of the measurements of central tendency in statistics. It's calculated by dividing the total number of observations by the sum of the observations. One of the measurements of dispersion is the standard deviation, which is used to show how much individuals in a group differ from the mean.

The z-score can be used to compare a student's performance when different types of scores are being considered.

The Z-score indicates how far a value is above or below the mean in terms of standard deviation. The $z$-score is calculated using the following formula:

$z=\frac{x-\mu }{\sigma }$

Where:

$\mathit{x}=$is any data value

$\mathit{\mu }=$is the population mean

$\sigma =$is the population standard deviation

We are given below information:

STUDENT	GPA	School average GPA	School standard deviation
Thuy	localid="1649446594289" $2.7$	$3.2$	$0.8$
Vichet	$87$	$75$	$20$
Kamala	localid="1649446601215" $8.6$	$8$	$0.4$

Now find the Z- score for the each of the above students.

The z-score for Thuy is:

$z=\frac{2.7-3.2}{0.8}=-0.625$

The z-score for Vichet is:

$z=\frac{87-75}{20}=0.6$

The z-score for Kamala is:

$z=\frac{8.6-8}{0.4}=1.5$

From the above calculations, we can see that Kamala's z-score is the highest of the three students; as a result, Kamala got the greatest GPA of the three students.