Assertion: Median of the given data 34, 31, 42, 43, 46, 25, 39, 45, 32 is $39$ .
Reason: When the number of observations $(n)$ is even, the median is the mean of the ${(\frac{n}{2})}^{t h}$ and ${(\frac{n}{2} + 1)}^{t h}$ observations.
Which of the following is correct?

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion

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Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is B Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
There are 9 observations and the ordered data is 25, 31, 32, 34, 39, 42, 43, 45, 46. By applying the formula for median when the number of values is odd, the median is at the 5th position which is 39. The reason is not the correct explanation of Assertion as the number of observations (n) is odd is not discussed.

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Similar questions

Assertion: Median of the given data $34, 31, 42, 43, 46, 25, 39, 45, 32$ , is $39$ .
Reason: When the number of observations $(n)$ is even, then median is the mean of the ${(\frac{n}{2})}^{t h}$ and ${(\frac{n}{2} + 1)}^{t h}$ observations.
Which of the following is correct?

Find the median of the following values :

37, 31, 42, 43, 46, 25, 39, 45, 32

Q. Mean deviation of

39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45

from their median is?

Q. Assertion : If the median of the given data 26, 29, 42, 53, x, x + 2, 70, 75, 82, 93, is 65 then the value of x is 64.
Reason : When the number of observations(n) is odd the median is the value of the

{(\frac{n + 1}{2})}^{t h}

observation.
Which of the following is correct.

Q. There are 2 sets of numbers in increasing order. The first set has ‘n’ numbers where ‘n’ is an odd number. The 2nd set has ‘m’ numbers where ‘m’ is an even number. The medians for both of the sets respectively is ______.

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Assertion: Median of the given data 34, 31, 42, 43, 46, 25, 39, 45, 32 is 39. Reason: When the number of observations (n) is even, the median is the mean of the (n2)th and (n2+1)th observations. Which of the following is correct?

Assertion: Median of the given data 34, 31, 42, 43, 46, 25, 39, 45, 32 is $39$ .
Reason: When the number of observations $(n)$ is even, the median is the mean of the ${(\frac{n}{2})}^{t h}$ and ${(\frac{n}{2} + 1)}^{t h}$ observations.
Which of the following is correct?