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24 Nov 2023, 09:36
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B
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In an exam, five students each receive a unique integer score between 0 and 100. If the median score is 70, what is the highest possible average (arithmetic mean) score?
A. 80.2
B. 81.2
C. 82.2
D. 83.2
E. 84.4
A. 80.2
B. 81.2
C. 82.2
D. 83.2
E. 84.4
In an exam, 5 people have different scores ranging from 0 to 100, inclusive. The scores are all integers. If the median score is 70, what is the greatest possible average (arithmetic mean) score?
24 Nov 2023, 22:06
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Five students each receive a unique integer score between 0 and 100 and the median score is 70
Since there are 5 students and median is 70
=> score of the middle or the 3rd student is 70
To make the average highest we need to have maximum value for all other scores
=> \(1^{st}\) student score = 68 ( 2 less than 70 as all scores are unique and this will be greatest value possible for the lowest score)
=> \(2^{nd}\) student score = 69 ( 1 less than 70 as all scores are unique and this will be greatest value possible for the second lowest score)
=> \(3^{rd}\) student score = 70 (Median)
=> \(4^{th}\) student score = 99 (1 less than maximum score possible which is 100)
=> \(5^{th}\) student score = 100 (maximum possible score)
=> Average = \(\frac{68 + 69 + 70 + 99 + 100 }{ 5}\) = \(\frac{406}{5}\) = 81.2
So, Answer will be B
Hope it helps!
Watch the following video to Learn the Basics of Statistics
Since there are 5 students and median is 70
=> score of the middle or the 3rd student is 70
To make the average highest we need to have maximum value for all other scores
=> \(1^{st}\) student score = 68 ( 2 less than 70 as all scores are unique and this will be greatest value possible for the lowest score)
=> \(2^{nd}\) student score = 69 ( 1 less than 70 as all scores are unique and this will be greatest value possible for the second lowest score)
=> \(3^{rd}\) student score = 70 (Median)
=> \(4^{th}\) student score = 99 (1 less than maximum score possible which is 100)
=> \(5^{th}\) student score = 100 (maximum possible score)
=> Average = \(\frac{68 + 69 + 70 + 99 + 100 }{ 5}\) = \(\frac{406}{5}\) = 81.2
So, Answer will be B
Hope it helps!
Watch the following video to Learn the Basics of Statistics
25 Nov 2023, 06:13
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To solve this question ,what we need to do is…
Let’s make the 5 exam scores as
Y,X,70,Z,A (let’s say this is from least to greatest)
X and Y will have to be smaller than 70,but be the largest it can be
So we will have
X=69 ( as it’s smaller than 70 but bigger than Y)
Y =68 (as it’s smaller than X)
Then let’s find the greatest possible numbers that Z and A can be.
Z = 99 (as it’s supposed to be smaller 100 and bigger than 70)
A = 100 (greatest number in the scores and the highest number you can get with the limit of 0-100)
Now to just find the mean we do
SUM OF TERMS/NUMBER OF TERMS
68 + 69 + 70 + 99 + 100 = 406
Then
406/5 = 81.2
Answer = B
Posted from my mobile device
Let’s make the 5 exam scores as
Y,X,70,Z,A (let’s say this is from least to greatest)
X and Y will have to be smaller than 70,but be the largest it can be
So we will have
X=69 ( as it’s smaller than 70 but bigger than Y)
Y =68 (as it’s smaller than X)
Then let’s find the greatest possible numbers that Z and A can be.
Z = 99 (as it’s supposed to be smaller 100 and bigger than 70)
A = 100 (greatest number in the scores and the highest number you can get with the limit of 0-100)
Now to just find the mean we do
SUM OF TERMS/NUMBER OF TERMS
68 + 69 + 70 + 99 + 100 = 406
Then
406/5 = 81.2
Answer = B
Posted from my mobile device
