Question

find the median of the data 24 ,65,85,12,45,35,85,85,15,16,​

Answer 1

$\sf\Large{\underline{\underline{Answer:-}}}$

$</p><p>\large{\sf{\green{\boxed{\: ★median =40}}}}</p><p></p><p>$

${\underline{\underline{\sf{\pink{Explaination,}}}}}$

Here, First we need to arrange the numbers in ascending order, we get

$\Longrightarrow$ 12, 15, 16, 24, 35, 45, 65, 85, 85, 85.

Number of terms, n = 10 (even)

We know that, when n is even we use this formula,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;Median\;=\;\bf{\dfrac{1}{2} \times (\frac{n}{2})^{th} \: term + (\frac{n}{2} + 1) ^{th} \: term}}\end{gathered}$

Substitute the values,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;=\;\bf{\dfrac{1}{2} \times (\frac{10}{2})^{th} \: term + (\frac{10}{2} + 1) ^{th} \: term}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;=\;\bf{\dfrac{1}{2} \times (5^{th} \: term \: + 6^{th} \: term) }}\end{gathered}$

We know that,

• 5th term = 35.
• 6th term = 45

${\underline{\underline{\sf{\green{Therefore;}}}}}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;=\;\bf{\dfrac{1}{2} \times(35 + 45) }}\end{gathered}$

$\: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;\;=\;\bf{\dfrac{1}{2} \times 80}}\end{gathered}$

$\: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\; Median\;=\;\bf{40 }}\end{gathered}$

$\sf\Large{\underline{\underline{Hence,}}}$

Median = 40

Answer 2

$\sf\Large{\underline{\underline{Answer:-}}}$

$</p><p>\large{\sf{\green{\boxed{\: ★median =40}}}}</p><p></p><p>$

${\underline{\underline{\sf{\pink{Explaination,}}}}}$

Here, First we need to arrange the numbers in ascending order, we get

$\Longrightarrow$ 12, 15, 16, 24, 35, 45, 65, 85, 85, 85.

Number of terms, n = 10 (even)

We know that, when n is even we use this formula,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;Median\;=\;\bf{\dfrac{1}{2} \times (\frac{n}{2})^{th} \: term + (\frac{n}{2} + 1) ^{th} \: term}}\end{gathered}$

Substitute the values,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;=\;\bf{\dfrac{1}{2} \times (\frac{10}{2})^{th} \: term + (\frac{10}{2} + 1) ^{th} \: term}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;=\;\bf{\dfrac{1}{2} \times (5^{th} \: term \: + 6^{th} \: term) }}\end{gathered}$

We know that,

5th term = 35.

6th term = 45

${\underline{\underline{\sf{\green{Therefore;}}}}}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;=\;\bf{\dfrac{1}{2} \times(35 + 45) }}\end{gathered}$

$\: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;\;=\;\bf{\dfrac{1}{2} \times 80}}\end{gathered}$

$\: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\; Median\;=\;\bf{40 }}\end{gathered}$

$\sf\Large{\underline{\underline{Hence,}}}$

Median = 40