Question

If the median of the data set 34, 37, 43, 50, x is 37 then the value of x is always _______.

A
greater than 50
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B
lies in between 37 and 43
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C
less than or equal to 37
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D
less than 34
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Solution

The correct option is C less than or equal to 37Median refers to the value which lies in the middle of the data when arranged in an increasing or decreasing order. There are 5 observations i.e., an odd number of observations and the value of the median is 37. So 37 will lie in the middle of the data. If 37 is the middle value, then x must come before 37 as 43, 50 are already greater than 37. There are two possible cases : 1st case : - 34, x, 37, 43, 50. 2nd case :- x, 34, 37, 43, 50. From 1st case, we can say that x should be less than or equal to 37. From 2nd case, we can say that x should be less than or equal to 34. Now considering the both cases, we can say that 'x' is always less than or equal to 37.

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