Question

consider the following test scores obtained by a class.
test score | 100 | 90 | 80 | 70 | 60 | 50
frequency | 2 | 8 | 12 | 5 | 4 | 2
find the range and mean (rounded to the nearest unit).
range
mean

Explanation:

Step1: Calculate the Range

The range is the difference between the maximum and minimum values. The maximum test score is 100, and the minimum is 50. So, range = 100 - 50 = 50.

Step2: Calculate the Mean

First, find the sum of (test score × frequency) for all scores.
For 100: \(100\times2 = 200\)
For 90: \(90\times8 = 720\)
For 80: \(80\times12 = 960\)
For 70: \(70\times5 = 350\)
For 60: \(60\times4 = 240\)
For 50: \(50\times2 = 100\)
Now, sum these products: \(200 + 720 + 960 + 350 + 240 + 100 = 2570\)
Next, find the total number of students (sum of frequencies): \(2 + 8 + 12 + 5 + 4 + 2 = 33\)
The mean is the total sum divided by the number of students: \(\frac{2570}{33} \approx 78\) (rounded to the nearest unit).

Answer:

range: 50
mean: 78