Question

2. Find the median of first 10 even numbers.​

Answer 1

2,4,6,8,10,12,14,16,18,20 are even. take them to be n

now n is even so n/2th observation +(n/2+1)2th ovservation

10/2th+(10/2+1)th.then 5th+6th/2

=19+12/2

=11

Answer 2

$\huge\color{pink}{\textbf{\textsf{Solution:-}}}$

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★ Given,

• Find the median of first 10 even numbers.

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We are asked to find the median of first 10 even numbers.

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We have,

• Number of terms (n) = 10 (even)
• Where, n is the number of terms.

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We know that if the n is even we use this formula,

${\sf {\purple{ \boxed{ \sf Median = \frac{1}{2}[ (\frac{n}{2}) ^{th} \: term + ( \frac{n}{2} + 1) ^{th} \: term] }}}}$

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First 10 even numbers are:- (must arranged in ascending order).

$\Longrightarrow$ 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 .

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On substituting the Values we get,

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

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

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Where,

• 5th term is 10
• 6th term is 12
• Put the Values accordingly,

$\: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;median\;=\;\bf{{ \frac{1}{2} \: (10 + 12)}\:}}\end{gathered}$

$\: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;median\;=\;\bf{{ \frac{1}{2} \times 22}\:}}\end{gathered}$

$\: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;median\;=\;\bf{{11}\:}}\end{gathered}$

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∴ Median is of first 10 even numbers is 11.