The formulae for calculating the median if individual observations are given will be.

(N + 1) / 2

th if n is add

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(N + 1) t h / 2

if n is even

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(N / 2)

th if n is even

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Both a & c

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Solution

The correct option is D Both a & c
Median is the middle most value of a series. So when the series has odd number of elements then median can be calculated easily but when the series has even number of elements then the series has two middle values, so median is calculated by taking out the average of both the value.

The series is first arranged into either ascending or descending order. The formula to calculate median = (N+1) /2 th term of the series in case odd numbers of data and median = N/2th term of the series in case even number of data where N is the number of observation in the series.

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Similar questions

Q. Which is false?
(a) If n is odd, then

median = value of (\frac{n + 1}{2}) th

item.
(b) If n is even, then

median = \frac{1}{2} \times \{value of \frac{n}{2} th item + value of (\frac{n}{2} + 1) th item\}

.
(c) Mode is the item which occurs most often.
(d)

Mode = \frac{1}{2} (mean + median)

For a n set of observations where n is odd the median is the ${\frac{n}{2}}^{t h}$ observation.

For a 'n' set of observations where 'n' is odd the median is the ${\frac{n}{2}}^{t h}$ observation.

Q. Find the

13^{t h}

and

16^{t h}

terms of the sequence defined by

b_{n} = {\begin{matrix} n^{2}, & i f n ϵ N and n is even n (n + 2), & i f n ϵ N and n is odd. \end{matrix}

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?

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