A class obtained the following scores on a test. Find the mean, the median, the mode, and the range for the class.
Test Score Frequency
90 2
80 3
70 10
60 5
50 3
40 2
(a) Find the mean.
1
(b) Find the median.
2
(c) Find the mode.
3
(d) Find the range.
4
0
What part of these questions don't you understand?
12
To find the mean, we need to calculate the sum of all the test scores and divide it by the total number of scores.
(a) Find the mean:
To calculate the mean, we multiply each test score by its frequency, then add up all the products. In this case, the calculations would be as follows:
(90 * 2) + (80 * 3) + (70 * 10) + (60 * 5) + (50 * 3) + (40 * 2) = 180 + 240 + 700 + 300 + 150 + 80 = 1650
Next, we divide this sum by the total number of test scores:
2 + 3 + 10 + 5 + 3 + 2 = 25
Mean = 1650 ÷ 25 = 66
Therefore, the mean score for the class is 66.
(b) Find the median:
The median is the middle value of the test scores, when they are arranged in numerical order. In this case, we can first list the test scores in increasing order:
40, 40, 50, 50, 50, 60, 60, 60, 60, 60, 70, 70, 70, 70, 70, 70, 70, 70, 70, 80, 80, 80, 90, 90
As we can see, there are 25 scores in total, which is an odd number. The median will be the 13th value, which is 70.
Therefore, the median score for the class is 70.
(c) Find the mode:
The mode is the value that appears most frequently in the data set. In this case, the mode is the test score with the highest frequency. Looking at the frequency column, we can see that the test score 70 has the highest frequency of 10.
Therefore, the mode for the class is 70.
(d) Find the range:
The range is the difference between the highest and lowest values in the data set. In this case, the highest score is 90, and the lowest score is 40.
Range = 90 - 40 = 50
Therefore, the range for the class is 50.