Question

plz tell the answers with step by step explanation....it's urgent​

Answer 1

GiveN:-

$\boxed{\begin{array}{|c|c|c|}\bf \: x&\bf \: f&\bf \: C.F.\\\dfrac{\qquad\qquad}{}&\dfrac{\qquad\qquad}{}&\dfrac{\qquad\qquad\qquad}{}\\\sf3&\sf5&\sf5\\\sf6&\sf2&\sf7\\\sf5&\sf4&\sf11\\\sf8&\sf6&\sf17\\\sf12&\sf7&\sf24\\\sf7&\sf6&\sf30\\\sf3&\sf2&\sf32\\&&\dfrac{\qquad\qquad}{}\\&&\bf32\end{array}}$

To FinD :-

The median and mode.

SolutioN:-

Here n(C.F.) = 32, which is even.

For even observations we know that our formula is,

$\normalsize{\underline{\boxed{\bf{Median=\left[\dfrac{\dfrac{n}{2}th\:observation+\left(\dfrac{n}{2}+1\right)th\:observation}{2}\right]n\:is\:even}}}}$

where,

• n is even = 32

Substituting the values,

$\\ :\normalsize\implies{\sf{Median=\left[\dfrac{\dfrac{32}{2}th\:observation+\left(\dfrac{32}{2}+1\right)th\:observation}{2}\right]}}$

$\\ :\normalsize\implies{\sf{Median=\left[\dfrac{16th\:observation+\left(16+1\right)th\:observation}{2}\right]}}$

$\\ :\normalsize\implies{\sf{Median=\left[\dfrac{16th\:observation+17th\:observation}{2}\right]}}$

$\\ :\normalsize\implies{\sf{Median=\left[\dfrac{8+8}{2}\right]}}$

(each observation from 12 to 17 have value 8)

$\\ :\normalsize\implies{\sf{Median=\left[\dfrac{16}{2}\right]}}$

$\\ :\normalsize\implies{\sf{Median=\left[\dfrac{\cancel{16}}{\cancel{2}}\right]}}$

$\\ \qquad\qquad\normalsize\therefore\boxed{\mathfrak{\pink{Median=8.}}}$

Mode :

According to the frequency table,

Variate 12 is having maximum frequency 7,

So the mode is 12.

_______________________________

Median = 8.

Mode = 12.

Answer 2

Answer:

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