Find the median of the following cumulative frequency distribution- x frequency Cumulative frequency- 22 1 1- 34 2 3- 39 2 5- 45 8 13- 54 8 21- 56 9 30- 68 4 34- 78 4 38- 84 2 40- -

Here, the sum of frequencies, n = 40, which is even. So, the median terms will be the n/2th and the (n/2+1)th observations, i.e. the 20th and the 21st observati ...

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Standard IX

Mathematics

Finding Median of Grouped Data When Class Intervals Are Not Given

Find the medi...

Question

Find the median of the following cumulative frequency distribution:
$\begin{matrix} x & f r e q u e n c y & C u m u l a t i v e f r e q u e n c y 22 & 1 & 1 34 & 2 & 3 39 & 2 & 5 45 & 8 & 13 54 & 8 & 21 56 & 9 & 30 68 & 4 & 34 78 & 4 & 38 84 & 2 & 40 \end{matrix}$

49.5

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53.5

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Solution

The correct option is C
54

Here, the sum of frequencies, n = 40, which is even.
So, the median terms will be the $\frac{n}{2} t h$ and the $(\frac{n}{2} + 1) t h$ observations, i.e. the 20th and the 21st observations.
Both the 20th and the 21st observations are 54.
So, the median term will be 54.

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Similar questions

Find the median term of the following cumulative frequency distribution:
$\begin{matrix} x & frequency & Cumulative frequency 22 & 1 & 1 34 & 2 & 3 39 & 2 & 5 45 & 8 & 13 54 & 8 & 21 56 & 9 & 30 68 & 4 & 34 78 & 4 & 38 84 & 2 & 40 \end{matrix}$

Q. Find the values of

a

b

c

and

d

in the given cumulative frequency distribution.

\begin{matrix} x & f r e q u e n c y & C u m u l a t i v e f r e q u e n c y 10 & 3 & a = - - - - 15 & 10 & b = - - - - 20 & 25 & c = - - - - 25 & 7 & d = - - - - 30 & 5 & 50 \end{matrix}

Q. Find the values of p, q, r and s in the given cumulative frequency distribution.

\begin{matrix} x & f r e q u e n c y & C u m u l a t i v e f r e q u e n c y 10 & 3 & p = - - - - 15 & 10 & q = - - - - 20 & 25 & r = - - - - 25 & 7 & s = - - - - 30 & 5 & 50 \end{matrix}

Q. [dummy - to replace with video] Find the mean deviaion about median for the following cumulative frequency distribution:

\begin{matrix} x & f r e q u e n c y & C u m u l a t i v e f r e q u e n c y 22 & 1 & 1 34 & 2 & 3 39 & 2 & 5 45 & 8 & 13 54 & 8 & 21 56 & 9 & 30 68 & 4 & 34 78 & 4 & 38 84 & 2 & 40 \end{matrix}

Q. Find the median class for the below distribution.

\begin{matrix} C l a s s & C u m u l a t i v e f r e q u e n c y 10 - 20 & 3 20 - 30 & 17 30 - 40 & 24 40 - 50 & 33 50 - 60 & 51 \end{matrix}

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Find the median of the following cumulative frequency distribution: xfrequencyCumulative frequency221134233925458135482156930684347843884240

The correct option is C 54 Here, the sum of frequencies, n = 40, which is even. So, the median terms will be the n2th and the (n2+1)th observations, i.e. the 20th and the 21st observations. Both the 20th and the 21st observations are 54. So, the median term will be 54.

Find the median of the following cumulative frequency distribution:
$\begin{matrix} x & f r e q u e n c y & C u m u l a t i v e f r e q u e n c y 22 & 1 & 1 34 & 2 & 3 39 & 2 & 5 45 & 8 & 13 54 & 8 & 21 56 & 9 & 30 68 & 4 & 34 78 & 4 & 38 84 & 2 & 40 \end{matrix}$

The correct option is C
54

Here, the sum of frequencies, n = 40, which is even.
So, the median terms will be the $\frac{n}{2} t h$ and the $(\frac{n}{2} + 1) t h$ observations, i.e. the 20th and the 21st observations.
Both the 20th and the 21st observations are 54.
So, the median term will be 54.