The mean is the average value of a given set of numbers, and the median is the number in the middle of a set of numbers arranged in increasing order
The correct values as response to the questions are;
The minimum possible <em>top score</em> is <u>21</u>
The maximum possible <em>top score</em> is <u>32</u>
The <em>minimum </em>of the possible <em>standard deviation</em> is approximately <u>1.26</u>
The <em>maximum </em>of the possible <em>standard deviation</em> is approximately <u>11.7</u>
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The reason the above values are correct are as follows:
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The given parameters are;
The number of students that take the test, n = 5
The amount of points for each problem = 1 point
The median score = 9
The mean Score = 10
Required:
The minimum possible score;
The maximum possible top score
The minimum of the possible standard deviations
The maximum of the possible standard deviations
Solution:
Given that there is a score (the median) which is 9, we have;
The scores obtainable in the test is Scores ≥ 9
Therefore, for a score of 10, we have;
The minimum total points obtainable = Mean × Number of students
Therefore;
Total minimum total points obtainable by the 5 students = 5 × 10 = 50
- The minimum possible top score
By arrangement, with the median at the middle, the minimum possible top score is given as follows;
0, 0, 9, 20, 21
Therefore, the minimum possible top score is <u>21</u>
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- The maximum possible top score
The maximum possible top score is similarly given by arrangement of the numbers as follows'
0, 0, 9, 9, 32
The maximum possible top score is <u>32</u>
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- The minimum standard deviation
By arrangement and selection, the minimum standard deviation is given as follows;
The minimum of the possible standard deviations of (9, 9, 9, 11, 12) ≈ <u>1.26</u>
- The maximum of the possible standard deviation
The maximum of the possible standard deviation is given as follows;
The maximum of the possible standard deviation of (0, 0, 9, 9, 32) ≈ <u>11.7</u>
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Learn more about mean and median here:
brainly.com/question/17012793
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