Find the median for the following frequency distribution- Age in years Number of people- 15 3- 16 8- 17 10- 18 10- 19 5- 20 4- -

[ nbsp; Age in years amp; Number of people amp; Cumulative frequency; 15 amp; 3 amp; 3; ...

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Byju's Answer

Standard XI

Statistics

Mean Deviation

Find the medi...

Question

Find the median for the following frequency distribution.

$\begin{matrix} A g e i n y e a r s & N u m b e r o f p e o p l e 15 & 3 16 & 8 17 & 10 18 & 10 19 & 5 20 & 4 \end{matrix}$
17

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Solution

The correct option is A 17
$\begin{matrix} A g e i n y e a r s & N u m b e r o f p e o p l e & C u m u l a t i v e f r e q u e n c y 15 & 3 & 3 16 & 8 & 11 17 & 10 & 21 18 & 10 & 31 19 & 5 & 36 20 & 4 & 40 \end{matrix}$
The total number of people is 40.
Since it is an even number,
there will be two median terms :
$(\frac{n}{2})^{t h}$ and $(\frac{n}{2} + 1) t h$ terms.
So, the median terms will be the 20th and 21st terms.
Both the 20th and 21st terms are 17.

Therefore, mean of both the terms = 17.

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Similar questions

In the given frequency distribution, median term(s) is/are ______.
$\begin{matrix} A g e i n y e a r s & N u m b e r o f p e o p l e 15 & 3 16 & 8 17 & 10 18 & 10 19 & 5 20 & 4 \end{matrix}$

In the given frequency distribution, which is the median term?
$\begin{matrix} Age in years & Number of people 15 & 3 16 & 8 17 & 10 18 & 10 19 & 5 20 & 4 \end{matrix}$

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

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$\begin{matrix} x & frequency & Cumulative frequency 22 & 1 & 1 34 & 2 & 3 39 & 2 & 5 45 & 8 & 13 54 & 8 & 21 56 & 9 & 30 68 & 4 & 34 78 & 4 & 38 84 & 2 & 40 \end{matrix}$

Question 3
A life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.

$\begin{matrix} A g e (i n y e a r s) & N u m b e r o f p o l i c y h o l d e r s B e l o w 20 & 2 B e l o w 25 & 6 B e l o w 30 & 24 B e l o w 35 & 45 B e l o w 40 & 78 B e l o w 45 & 89 B e l o w 50 & 92 B e l o w 55 & 98 B e l o w 60 & 100 \end{matrix}$

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Find the median for the following frequency distribution. Age in yearsNumber of people1531681710181019520417

Find the median for the following frequency distribution.

$\begin{matrix} A g e i n y e a r s & N u m b e r o f p e o p l e 15 & 3 16 & 8 17 & 10 18 & 10 19 & 5 20 & 4 \end{matrix}$
17