Question

in a mathematics test given to 15 students the following marks out of 100 are recorded 41 39 48 52 46 62 54 40 96 52 98 40 42 52 60 find the mean median mode
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Answer 1

AnsweR :

$\bf{\Large{\underline{\sf{Given\::}}}}$

In a mathematics test given to 15 students the following out of 100 are recorded 41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60.

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

• Mean
• Median
• Mode.

$\bf{\Large{\underline{\rm{\purple{Explanation\::}}}}}$

Formula use :

$\bf{\large{\boxed{\sf{Mean\:=\:{\it\dfrac{Sum\:of\:all\:Data\:point}{Number\:of\:data\:point} }}}}}}$

A/q

$|\implies\sf{Mean\:=\:\dfrac{41+39+48+52+46+62+54+40+96+52+98+40+42+52+60}{15} }\\\\\\\\|\implies\sf{Mean\:=\:\dfrac{822}{15} }\\\\\\\\|\implies\sf{Mean\:=\:\cancel{\dfrac{822}{15} }}\\\\\\\\|\implies\sf{\orange{Mean\:=\:54.8}}$

$\bigstar\sf{\large{\underline{Median\::}}}}}$

Firstly, arranging given data in ascending order :

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98.

If the number of observations (n) is odd.   [Given = 15]

Then, formula use :

$\bf{\large{\boxed{\sf{Median\:=\:\bigg(\frac{n+1}{2} \bigg)^{th} observation}}}}}$

A/q

$|\implies\sf{Median\:=\:\bigg(\dfrac{15+1}{2} \bigg)^{th} observation}\\\\\\\\|\implies\sf{Median\:=\:\bigg(\cancel{\dfrac{16}{2} }\bigg)^{th} observation}\\\\\\\\|\implies\sf{Median\:=\:8^{th} \:observation}\\\\\\\\|\implies\sf{\orange{Median\:=\:52}}$

$\bigstar\sf{\large{\underline{Mode\::}}}}}$

We know that the highest common number to given observation.

Here;

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

Since, 52 occur many times or most often in a set of data.

∴ Mode = 52

Answer 2

$\huge\bold{Question}$

In a mathematics test given to 15 students the following marks out of 100 are recorded 41 39 48 52 46 62 54 40 96 52 98 40 42 52 60 find the mean median mode

$\huge\bold{AnsWer}$

Simply by using Formula →

Mean = sum of all data / Total No. data value

$\begin{lgathered}\tt{Mean\:=\:\dfrac{41+39+48+52+46+62+54+40+96+52+98+40+42+52+60}{15} }\\\\\\\\\tt{Mean\:=\:\dfrac{822}{15} }\\\\\\\\\tt{Mean\:=\:\cancel{\dfrac{822}{15} }}\\\\\\\\\sf{Mean\:=\:54.8}\end{lgathered}$

Firstly, arranging given data in ascending order :

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98.

If the number of observations (n) is odd. [Given = 15]

Then, simply by using the formula : →

Median = ( n +1 / 2 ) ²

$\begin{lgathered}\tt{Median\:=\:\bigg(\dfrac{15+1}{2} \bigg)^{th} observation}\\\\\\\\\tt{Median\:=\:\bigg(\cancel{\dfrac{16}{2} }\bigg)^{th} observation}\\\\\\\\\sf{Median\:=\:8^{th} \:observation}\\\\\\\\\tt{Median\:=\:52}\end{lgathered}$

As , We know that the highest common number to given observation.

Hence :- 39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

Since, 52 repeats many times or most often in a set of data.

Hence, the Mode is = 52