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28 Jun 2023, 00:12
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In a certain district, the minimum of the monthly rainfall is 0.2, max is 12.2 and the average of 12 months is 3.5. Which of the following is the greatest possible value of the median?
A. 2.4
B. 3.5
C. 4.2
D. 4.8
E. 6.2
A. 2.4
B. 3.5
C. 4.2
D. 4.8
E. 6.2
01 Jul 2023, 05:08
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In a certain district, the minimum of the monthly rainfall is 0.2, max is 12.2 and the average of 12 months is 3.5. Which of the following is the greatest possible value of the median?
Sum = 3.5 * 12 = 42
Since, we need to find the greatest possible value of the median, we first arrange the values in ascending order, and take the average of the 6th n 7th value.
To maximize the median, we need to keep the first five readings to the minimum which is 0.2 and maximize the readings from 6th - 11th.
the sum of first five readings = 0.2*5 = 1
Now the maximum is 12.2, hence, we are left with (42 - 12.2 - 1 =) 28.8 to be equally distributed among 6-11th values.
the average = 28.8/6 = 4.8
Answer D
Sum = 3.5 * 12 = 42
Since, we need to find the greatest possible value of the median, we first arrange the values in ascending order, and take the average of the 6th n 7th value.
To maximize the median, we need to keep the first five readings to the minimum which is 0.2 and maximize the readings from 6th - 11th.
the sum of first five readings = 0.2*5 = 1
Now the maximum is 12.2, hence, we are left with (42 - 12.2 - 1 =) 28.8 to be equally distributed among 6-11th values.
the average = 28.8/6 = 4.8
Answer D
29 May 2024, 03:37
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧
In a certain district, the minimum of the monthly rainfall is 0.2, max is 12.2 and the average of 12 months is 3.5
Min = 0.2
Max = 12.2
Mean (Average) = 3.5
Number of months = 12
=> Sum = mean * number of months = 3.5 * 12 = 42
Since there are 12 values so median = Mean of \(6^{th}\) and \(7^{th}\) term (after arranging the terms in ascedning or descending order)
= \(\frac{6^{th} + 7^{th}}{2}\)
And we have to find the maximum value of the median
=> we need to find the maximum value of the \(6^{th}\) and the \(7^{th}\) term
Since we know the sum of the terms so the \(6^{th}\) and the \(7^{th}\) term will be maximum when all the terms from \(2^{nd}\) to \(5^{th}\) term should be as small as possible
=> \(2^{nd}\) = \(3^{rd}\) = \(4^{th}\) = \(5^{th}\) term = \(1^{st}\) term = Min = 0.2
Now for the \(6^{th}\) and \(7^{th}\) term to be greatest we can make all the terms from \(8^{th}\) to \(11^{th}\) the least
But, these terms will be at least equal to \(7^{th}\) term and the \(6^{th}\)
=> \(6^{th}\) = \(7^{th}\) = \(8^{th}\) = \(9^{th}\) = \(10^{th}\) = \(11^{th}\) = x
=> Sum of all the terms = 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + x + x + x + x + x + x + 12.2 = 42
=> 5 * 0.2 + 6*x + 12.2 = 42
=> 6x = 42 - 1 - 12.2
=> 6x = 28.8
=> x = \(\frac{28.8}{6}\) = 4.8
So, Answer will be D
Hope it helps!
Watch the following video to MASTER Statistics
In a certain district, the minimum of the monthly rainfall is 0.2, max is 12.2 and the average of 12 months is 3.5
Min = 0.2
Max = 12.2
Mean (Average) = 3.5
Number of months = 12
=> Sum = mean * number of months = 3.5 * 12 = 42
Since there are 12 values so median = Mean of \(6^{th}\) and \(7^{th}\) term (after arranging the terms in ascedning or descending order)
= \(\frac{6^{th} + 7^{th}}{2}\)
And we have to find the maximum value of the median
=> we need to find the maximum value of the \(6^{th}\) and the \(7^{th}\) term
Since we know the sum of the terms so the \(6^{th}\) and the \(7^{th}\) term will be maximum when all the terms from \(2^{nd}\) to \(5^{th}\) term should be as small as possible
=> \(2^{nd}\) = \(3^{rd}\) = \(4^{th}\) = \(5^{th}\) term = \(1^{st}\) term = Min = 0.2
Now for the \(6^{th}\) and \(7^{th}\) term to be greatest we can make all the terms from \(8^{th}\) to \(11^{th}\) the least
But, these terms will be at least equal to \(7^{th}\) term and the \(6^{th}\)
=> \(6^{th}\) = \(7^{th}\) = \(8^{th}\) = \(9^{th}\) = \(10^{th}\) = \(11^{th}\) = x
=> Sum of all the terms = 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + x + x + x + x + x + x + 12.2 = 42
=> 5 * 0.2 + 6*x + 12.2 = 42
=> 6x = 42 - 1 - 12.2
=> 6x = 28.8
=> x = \(\frac{28.8}{6}\) = 4.8
So, Answer will be D
Hope it helps!
Watch the following video to MASTER Statistics
