Question

You have just given students a twenty-question quiz. Consider the following scores as the number of correct responses for ten students on the quiz: 8, 16, 14, 7, 11, 15, 19, 10, 5, 15. Which of the following correctly depicts the statistics for this distribution?

a) Mean = 11.0; Median = 12.5; Mode = 15.0
b) Mean = 11.0; Median = 11.0; Mode = 15.0
c) Mean = 11.0; Median = 14.0; Mode = 15.0
d) Mean = 11.0; Median = 11.0; Mode = 11.0

Answer 1

After calculating the statistics for the given dataset, the correct mean is 12.0, the median is 12.5, and the mode is 15.0. However, none of the answer choices provided by the student match these calculations, as all options have an incorrect mean of 11.0.

Step-by-step explanation:

To determine which option correctly depicts the statistics for the distribution of quiz scores, we need to calculate the mean, median, and mode of the given dataset: 8, 16, 14, 7, 11, 15, 19, 10, 5, 15.

1. Mean: The mean is the average of the scores. To calculate the mean, sum all the scores and divide by the number of scores. Mean = (8 + 16 + 14 + 7 + 11 + 15 + 19 + 10 + 5 + 15) / 10 = 120 / 10 = 12.0.
2. Median: The median is the middle value when the data is ordered. After ordering the scores (5, 7, 8, 10, 11, 14, 15, 15, 16, 19), the middle scores are the 5th and 6th scores, which are 11 and 14. Median = (11 + 14) / 2 = 25 / 2 = 12.5.
3. Mode: The mode is the most frequently occurring score, which is 15 as it appears twice in the dataset.

Therefore, the correct depiction of the statistics for this distribution would be: Mean = 12.0; Median = 12.5; Mode = 15.0.

The student has made a mistake in computing the mean. None of the given options a), b), c), or d) has the correct mean. Since the correct mean is 12.0 and not 11.0 as stated in all options, none of the options provided by the student is correct.