Question

representing data with mean and median
mr. singh needed to understand the trend of his students’ latest test scores. find the mean and median for each set of data, and then determine which gives a better picture of the scores.
scores: 89, 99, 80, 5, 90, 0, 100, 95
the mean test score is
the median test score is
which measure of center best represents the test data?
mean
median
both mean and median
neither mean nor median

Explanation:

Step1: Calculate the Mean

First, sum all the test scores: \( 89 + 99 + 80 + 5 + 90 + 0 + 100 + 95 \). Let's compute that: \( 89 + 99 = 188 \), \( 188 + 80 = 268 \), \( 268 + 5 = 273 \), \( 273 + 90 = 363 \), \( 363 + 0 = 363 \), \( 363 + 100 = 463 \), \( 463 + 95 = 558 \). There are 8 scores, so the mean is \( \frac{558}{8} = 69.75 \).

Step2: Calculate the Median

First, order the scores from least to greatest: \( 0, 5, 80, 89, 90, 95, 99, 100 \). Since there are 8 (an even number) scores, the median is the average of the 4th and 5th values. The 4th value is 89, the 5th is 90. So the median is \( \frac{89 + 90}{2} = \frac{179}{2} = 89.5 \).

Step3: Determine Best Measure

The mean is affected by the very low scores (0 and 5), which are outliers. The median is less affected by outliers and better represents the typical score of the majority of students (most scores are in the 80 - 100 range). So the median is a better measure.

Answer:

The mean test score is \( 69.75 \).
The median test score is \( 89.5 \).
Which measure of center best represents the test data? median