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A
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Difficulty:
45%
(medium)
Question Stats:
58% (01:07) correct
42%
(01:14)
wrong
based on 219
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History
Date
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Is the standard deviation of prices (per share) of 10 stocks less than $50?
(1) The highest price is $80, and the lowest price is $50.
(2) The average of price of the 10 stocks is $60.
(1) The highest price is $80, and the lowest price is $50.
(2) The average of price of the 10 stocks is $60.
11 Jan 2019, 20:07
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Is the standard deviation of prices (per share) of 10 stocks less than $50?
(1) The highest price is $80, and the lowest price is $50.
Highest and Lowest price are given, implies range = 30$
All the prices of remaining stocks lie with in the range and the mean as well
50 < mean < 80
standard deviation = \(\sqrt{Sum of((x- mean))^2/10}\)
(x-mean) < 30
Let us consider the extreme case,
Sum of all (x-mean)^2 < (10*(30)^2)/10 < (30)^2
Taking square root of 30^2 gives the standard deviation, which is always less than $50
Sufficient
(2) The average of price of the 10 stocks is $60.
We have no idea of the 10 stock prices, they may vary by high difference making standard deviation > 50 or vary by very less difference making standard deviation < $50
Insufficient
Option A is correct
(1) The highest price is $80, and the lowest price is $50.
Highest and Lowest price are given, implies range = 30$
All the prices of remaining stocks lie with in the range and the mean as well
50 < mean < 80
standard deviation = \(\sqrt{Sum of((x- mean))^2/10}\)
(x-mean) < 30
Let us consider the extreme case,
Sum of all (x-mean)^2 < (10*(30)^2)/10 < (30)^2
Taking square root of 30^2 gives the standard deviation, which is always less than $50
Sufficient
(2) The average of price of the 10 stocks is $60.
We have no idea of the 10 stock prices, they may vary by high difference making standard deviation > 50 or vary by very less difference making standard deviation < $50
Insufficient
Option A is correct
12 Jan 2019, 10:26
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Yes, is this an official question? I doubt that they would ask to find the value of a standard deviation, and even more if the SD is so big given the range.
