The table below shows the scores of a group of students on a 10-point quiz.
Test Score Frequency
3 0
4 2
5 2
6 1
7 2
8 3
9 0
10 4
The mean score on this test is:
The median score on this test is
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To find the mean score on the test, you will need to calculate the sum of the scores and divide by the total number of scores.
The sum of the scores can be calculated by multiplying each score by its corresponding frequency and then adding up these products:
(4 * 2) + (5 * 2) + (6 * 1) + (7 * 2) + (8 * 3) + (10 * 4) = 8 + 10 + 6 + 14 + 24 + 40 = 102
The total number of scores is the sum of the frequencies:
0 + 2 + 2 + 1 + 2 + 3 + 0 + 4 = 14
The mean score is then calculated by dividing the sum of the scores by the total number of scores:
Mean score = 102 / 14 = 7.29
Therefore, the mean score on this test is approximately 7.29.
To find the median score on the test, you will need to arrange the scores in ascending order and find the middle score.
Arranging the scores in ascending order:
3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 8, 10, 10, 10, 10
Since there are 14 scores, the middle score is the 7th score:
Median score = 6
Therefore, the median score on this test is 6.
To find the mean score on this test, you need to calculate the sum of all the scores and divide it by the total number of scores.
To calculate the sum, you multiply each score by its respective frequency and then add them all together.
In this case, you would calculate:
(4*2) + (5*2) + (6*1) + (7*2) + (8*3) + (10*4) = 8 + 10 + 6 + 14 + 24 + 40 = 102
Since the total number of scores is equal to the sum of the frequencies, which is 2 + 2 + 1 + 2 + 3 + 4 = 14, you divide the sum by 14 to find the mean:
Mean = 102 / 14 = 7.29 (rounded to two decimal places)
Therefore, the mean score on this test is approximately 7.29.
To find the median score on this test, you need to arrange the scores in ascending order.
Using the table, the scores in ascending order are: 4, 4, 5, 5, 6, 7, 7, 8, 8, 8, 10, 10, 10, 10.
To find the median, you need to identify the middle score(s) of the ordered list. Since the total number of scores is 14, the middle score(s) will be the 7th and 8th scores (or the average of the two middle scores if there is an even number of scores in the data set).
In this case, the median score is (6 + 7) / 2 = 6.5
Therefore, the median score on this test is 6.5.