Question

a student recorded her scores on weekly math quizzes that were marked out of a possible 10 points. her scores were as follows: 8, 5, 8, 5, 7, 6, 7, 7, 5, 7, 5, 5, 6, 6, 9, 8, 9, 7, 9, 9, 6, 8, 6, 6, 7. what is the mean of her test scores? what is the median of her test scores?

Explanation:

Step1: Calculate sum of scores

$8 + 5+8 + 5+7 + 6+7 + 7+5 + 7+5 + 6+6 + 9+8 + 9+7 + 9+9 + 6+8 + 6+6 + 7=168$

Step2: Determine number of scores

There are 24 scores.

Step3: Calculate the mean

The mean $\bar{x}=\frac{168}{24}=7$

Step4: Arrange scores in ascending order

$5,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,9,9,9,9,9$

Step5: Find the median

Since $n = 24$ (even), the median is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th ordered values. $\frac{n}{2}=12$ and $\frac{n}{2}+1 = 13$. The 12 - th value is 7 and the 13 - th value is 7. So the median is $\frac{7 + 7}{2}=7$

Answer:

Mean: 7
Median: 7