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02 Feb 2022, 03:00
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Difficulty:
35%
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66% (01:25) correct
34%
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wrong
based on 102
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{x1,x2,x3…x9} and {y1,y2,y3…y9} are two evenly spaced sets having 9 elements each. What is the difference between their standard deviations?
(1) \(x_2–x_1=3\) and \(y_9–y_8=2\)
(2) \(x_1=8\), \(x_9=32\) and \(y_1=2\), \(y9=18\)
(1) \(x_2–x_1=3\) and \(y_9–y_8=2\)
(2) \(x_1=8\), \(x_9=32\) and \(y_1=2\), \(y9=18\)
kungfury42
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02 Feb 2022, 17:49
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(1) x2-x1 = 3 and y9-y8 = 2
>> This means that all elements in the first set are 3 units apart and all elements in the second set are 2 units apart.
>> Since we know that each set has equally spaced elements and that there are a total of 9 elements in each, the 5th element of the set will be the arithmetic mean of the 9 elements of the set.
>> Mean = x5 and y5
>> Formula for standard deviation requires (sum of squares of) distance of each element from the mean which can now be easily calculated using the above points.
>> Hence, we can calculate the standard deviations for sets x and y and their difference.
>> (1) is sufficient.
(2) x1 = 8, x9 = 32, y1 = 2, and y9 = 18
>> Since we know that the sets are evenly spaced, the distance between the 1st and the 9th elements will be equal to 8 times the space between consecutive elements in the set.
>> Therefore, x9 - x1 = 24 = 8(x2 - x1) which means x2 - x1 = 3
>> Similarly y9 - y1 = 16 = 8(y2 - y1) which means y2 - y1 = 2
>> We arrive at the same point where statement 1 starts.
>> (2) is also sufficient.
...
Hence, either statement alone is sufficient (D)
Posted from my mobile device
>> This means that all elements in the first set are 3 units apart and all elements in the second set are 2 units apart.
>> Since we know that each set has equally spaced elements and that there are a total of 9 elements in each, the 5th element of the set will be the arithmetic mean of the 9 elements of the set.
>> Mean = x5 and y5
>> Formula for standard deviation requires (sum of squares of) distance of each element from the mean which can now be easily calculated using the above points.
>> Hence, we can calculate the standard deviations for sets x and y and their difference.
>> (1) is sufficient.
(2) x1 = 8, x9 = 32, y1 = 2, and y9 = 18
>> Since we know that the sets are evenly spaced, the distance between the 1st and the 9th elements will be equal to 8 times the space between consecutive elements in the set.
>> Therefore, x9 - x1 = 24 = 8(x2 - x1) which means x2 - x1 = 3
>> Similarly y9 - y1 = 16 = 8(y2 - y1) which means y2 - y1 = 2
>> We arrive at the same point where statement 1 starts.
>> (2) is also sufficient.
...
Hence, either statement alone is sufficient (D)
Posted from my mobile device
23 Oct 2023, 20:28
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