Question

Two classes took the same math test. In one class, the high score was 98% and the low score was 75%. In the other class, the high score was 96% and the low score was 51%. Explain what each measure of measure of central tendency could tell you about these class scores and the comparison of how the two classes did on the test? Explain your reasoning.

Answer 1

Measures of central tendency like the mean, median, and mode provide different insights into the performance of two classes on a math test. The range and standard deviation would further help to understand the variability of the scores within each class.

Step-by-step explanation:

When comparing the test scores of two classes on the same math test using measures of central tendency, each measure provides different insights. The mode, median, and mean reveal varying aspects of the classes' performance. For example, class one's high score was 98% and the low score was 75%, while the second class had a high score of 96% and a low score of 51%. Comparing the mean scores would tell us the average performance of each class. The median would provide the middle score, showing the central performance while minimizing the effect of extreme scores. The mode might not be as informative unless there are scores that occur with high frequency. Notably, statistics like the range, which in this case would be 23% for the first class and 45% for the second, give us an idea of the variability of scores within each class. The standard deviation could provide additional insights into how spread out the scores are around the mean. The larger the range and standard deviation, the greater the variability in test scores.