Question

A teacher notices that, on the last science test, some students did very well while other students performed poorly or had grades in the middle of the pack. If she wanted to measure how 'spread out' all the scores were, which descriptive statistic could she use?

A. Mean
B. Median
C. Range
D. Experimental Group

Answer 1

Option (C), To measure how 'spread out' test scores are, a teacher could use range or standard deviation. Range shows the difference between the highest and lowest scores, while standard deviation measures how much scores deviate from the average.

Step-by-step explanation:

If a teacher wants to measure how 'spread out' all the test scores were, she could use range or standard deviation as descriptive statistics. Range gives a measure of the overall spread between the highest and lowest scores, while standard deviation gives a measure of how spread out the scores are around the mean score.

Given the scenario where some students did very well and others performed poorly, with grades also in the middle, the teacher would find that the standard deviation is a useful statistic. It would provide a numerical value expressing the average distance of each score from the mean, reflecting the variation of scores in the class.

To compute the standard deviation, the teacher would follow these steps using the sample formula for standard deviation:

1. Calculate the mean (average) of the test scores.
2. Subtract the mean from each test score to get the deviation for each score.
3. Square each of these deviations.
4. Add up all the squared deviations.
5. Divide this sum by the number of scores minus one (n-1) to get the variance.
6. Take the square root of the variance to get the standard deviation.