Problem 3

Question

In the following set of test scores, what is the mode and what is the range? Test Scores: \(71,67,75,65,66,32,69,70,72,82,\) 73,68,75,68,75,78 (A) Mode: 68; Range: 75 (B) Mode: 69; Range: 50 (C) Mode: 75; Range: 70.5 (D) Mode: 75; Range: 50

Step-by-Step Solution

Verified
Answer
(D) Mode: 75; Range: 50
1Step 1: Organize the data
Arrange the test scores in ascending order for easier analysis: 32, 65, 66, 67, 68, 68, 69, 70, 71, 72, 73, 75, 75, 75, 78, 82.
2Step 2: Count the occurrences of each score
Count how many times each score appears in the set to find the mode: 32 - 1 time, 65 - 1 time, 66 - 1 time, 67 - 1 time, 68 - 2 times, 69 - 1 time, 70 - 1 time, 71 - 1 time, 72 - 1 time, 73 - 1 time, 75 - 3 times, 78 - 1 time, 82 - 1 time. The mode is the number that appears most often, which in this case is 75 with 3 occurrences.
3Step 3: Find the range
The range is the difference between the highest and lowest values in the set. In this set of test scores, the lowest value is 32, and the highest value is 82. So the range is: \(82 - 32 = 50\). Thus, the mode is 75, and the range is 50. The correct answer is (D) Mode: 75; Range: 50.