Question

open - ended problem: w respond fully to the open - ended question that follows. show mathematical work. then briefly explain your method and clearly identify your answer(s) on the lines provided. use complete sentences. the chart shows the scores for a high school calculus test. find the mean, median, mode, and range of the class scores.

# of students	overall grade
4	85
8	72
3	63
2	53

mean: ____
median: ____
mode: ____
range: ____

Explanation:

Step1: Calculate total score

\[5\times96 + 4\times85+8\times72 + 3\times63+2\times53=480+340 + 576+189+106 = 1691\]

Step2: Calculate total number of students

\[5 + 4+8+3+2=22\]

Step3: Calculate the mean

The mean $\bar{x}=\frac{1691}{22}\approx76.86$

Step4: Arrange scores in ascending - order and find median

First, list out all the scores: 53, 53, 63, 63, 63, 72, 72, 72, 72, 72, 72, 72, 72, 85, 85, 85, 85, 96, 96, 96, 96, 96. There are 22 scores. The median is the average of the 11th and 12th - ordered scores. The 11th and 12th scores are both 72, so the median is 72.

Step5: Find the mode

The score 72 appears 8 times, more frequently than any other score, so the mode is 72.

Step6: Calculate the range

The range is the difference between the highest and lowest scores. Range = 96 - 53=43

Answer:

Mean: approximately 76.86
Median: 72
Mode: 72
Range: 43