Z SCORE ASSIGNMENT HELP

This is one of the many statistical values that you will often interact with. A Z-Score tells you by how many standard deviations the value you are considering is from the population mean. If you are considering a large random data sample, you are guaranteed that 95 percent of the values will fall between -2 and 2 standard deviations from the mean.

To find the Z-Score for an element, subtract the population mean from the element and then divide the result obtained by the standard deviation i.e.,

Z=(X-μ)/σ

This is especially useful when you are gauging for example your performance in two subjects and you want to know in which test you performed better.

Case Study

Lets’ take a case scenario where a student had a score of 87 in a music test and 59 in a math exam. Let’s also assume that the mean scores for the two classes were 85 and 41 respectively. In addition, the standard deviations were 13 and 11 respectively. In which subject did the student perform better?

Answer

We need to find the Z-Score to answer this question.

Z-Score from music test
Z=(87-85)/13=2/13=0.15
Z-Score from math exam
Z=(59-41)/11=18/11=1.64

From the above results, it is now clear that the student performed better in the math exam as compared to the music test.

Analysis

Three outcomes are possible:

Z-Score = 0: Value of element equal to mean.
Z-Score > 0: Value of element greater than mean.
Z-Score < 0: Value of element less than mean.