Question

derrick needs to figure out how hes doing on his test scores so far this year. you can help by calculating the mean and the median to get an overall picture of his scores. below are all of his scores: 25, 40, 68, 85, 95, 98, 70, 78, 85, 100. what is derricks mean test score so far? what is derricks median test score so far? which gives a better picture of his scores?

Explanation:

Step1: Arrange scores in ascending order

25, 40, 68, 70, 78, 85, 85, 95, 98, 100

Step2: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 10$ and $\sum_{i=1}^{10}x_{i}=25 + 40+68+70+78+85+85+95+98+100 = 744$. So, $\bar{x}=\frac{744}{10}=74.4$

Step3: Calculate the median

Since $n = 10$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The 5th value is 78 and the 6th value is 85. Median $=\frac{78 + 85}{2}=81.5$

Step4: Analyze which is better

The mean is affected by the low score of 25. The median is less affected by extreme values. So the median gives a better picture of his performance.

Answer:

Derrick's mean test score so far is 74.4.
Derrick's median test score so far is 81.5.
The median gives a better picture of his scores.