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
To find the mean, add up the scores and divide by 14.
To find the median, arrange the scores in order. The middle score is the median.
To find the mean score on this test, we need to multiply each score by its corresponding frequency (the number of students who achieved that score), then sum up these values and divide by the total number of students.
Let's calculate it step-by-step:
1. Multiply each score by its corresponding frequency:
4 x 2 = 8
5 x 2 = 10
6 x 1 = 6
7 x 2 = 14
8 x 3 = 24
10 x 4 = 40
2. Sum up the above values:
8 + 10 + 6 + 14 + 24 + 40 = 102
3. Divide the sum by the total number of students (which can be found by summing up the frequencies):
0 + 2 + 2 + 1 + 2 + 3 + 0 + 4 = 14
Mean score = 102 / 14 = 7.29 (rounded to two decimal places)
Therefore, the mean score on this test is 7.29.
To find the median score on this test, we need to arrange the scores in ascending order and find the middle value. If there is an even number of scores, we will take the average of the two middle values.
Let's calculate it step-by-step:
1. Arrange the scores in ascending order:
3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 8, 10, 10, 10, 10
2. Find the middle value(s):
In this case, there are 14 scores, so we find the average of the two middle values:
(6th value + 7th value) / 2 = (6 + 7) / 2 = 6.5
Therefore, the median score on this test is 6.5.
To find the mean score, you need to calculate the sum of all the scores and divide it by the total frequency.
First, multiply each test score by its corresponding frequency:
4 * 2 = 8
5 * 2 = 10
6 * 1 = 6
7 * 2 = 14
8 * 3 = 24
9 * 0 = 0
10 * 4 = 40
Next, add up all these products:
8 + 10 + 6 + 14 + 24 + 0 + 40 = 102
Then, divide this sum by the total frequency:
2 + 2 + 1 + 2 + 3 + 0 + 4 = 14
Mean score = 102 / 14 = 7.29 (approximately)
So the mean score on this test is approximately 7.29.
To find the median score, you need to arrange all the scores in ascending order and find the middle value. If there is an even number of scores, you need to calculate the average of the two middle values.
Arranging the scores in ascending order: 4, 4, 5, 5, 6, 7, 7, 8, 8, 8, 10, 10, 10, 10
Since there are 14 scores, the middle two values are the 7th and 8th scores, which are both 7.
Therefore, the median score on this test is 7.