A student got these marks on 7math tests:
91%,75%,95%,,80%,83%,86%,68%
What mark will the student need on the 8th test to make each statement true?
a)The mean of the tests is 84%
b)The mode of the eight tests is 86%
c)The median of the eight tests is 84%
To find out what mark the student will need on the 8th test to make each statement true, we can follow these steps:
a) To find the mean, we add up all the test scores and divide by the total number of tests.
Mean = (91 + 75 + 95 + 80 + 83 + 86 + 68 + X) / 8
To make the mean 84%, we can set up the equation:
(91 + 75 + 95 + 80 + 83 + 86 + 68 + X) / 8 = 84
510 + X = 672
X = 672 - 510
X = 162
Therefore, the student will need to score 162% on the 8th test to make the mean 84%.
b) To find the mode, we need to identify the score that appears most frequently. In this case, we have two scores, 86 and X. To make the mode 86%, we need the score X to be 86. Therefore, the student will need to score 86% on the 8th test to make the mode 86%.
c) To find the median, we need to arrange the test scores in order and find the middle value. The given 7 test scores are: 68, 75, 80, 83, 86, 91, 95, and the middle value is the 4th score, which is 83. To make the median 84%, we need the 8th score to be higher than 83%. Therefore, the student will need to score higher than 83% on the 8th test to make the median 84%.
To solve this problem, we need to find the mark that the student needs to achieve on the 8th test to meet the given conditions. Let's follow these steps:
a) To find the mean, we need to calculate the sum of all the test scores and divide it by the number of tests. We already have 7 test scores, so let's calculate the current sum:
91 + 75 + 95 + 80 + 83 + 86 + 68 = 568
Now, let's calculate the current mean:
568 / 7 = 81.14%
To find the mark the student needs on the 8th test, we can use the formula:
(Desired mean * Total number of tests) - Current sum = Required mark on the 8th test
(84% * 8) - 568 = Required mark on the 8th test
672 - 568 = Required mark on the 8th test
104 = Required mark on the 8th test
Therefore, the student needs to score 104% on the 8th test to make the mean of all the tests equal to 84%.
b) To find the mode, we need to check which test score appears most frequently. In this case, the number 86 appears twice, which is the highest frequency among all the scores. Since the 8th test has not been taken yet, the current mode holds. Hence, the mode of the eight tests is 86%.
c) To find the median, we need to arrange the test scores in ascending order:
68, 75, 80, 83, 86, 91, 95
Since we have an odd number of test scores (7), the median is the middle value. In this case, the median is 83%.
To make the median of the eight tests equal to 84%, the student would need to score 84% on the 8th test.
In summary, the student will need to score 104% on the 8th test to make the mean of the tests 84%, the mode of the eight tests will be 86%, and the median of the eight tests will be 84%.
This should help you:
Mean = Σscores/number of scores = (All the scores +8th)/8
Mode is the most frequently occurring score.
Median is 50th percentile, so you need as many score below 84% as above.