Question

The runs scored by a cricket team in 11 matches are as follow:-

90,40,30,110,80,20,30,15,30,10,8. Find the mean ,mode and median of the data.

Also state whether they are same or not ?
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Answer 1

Answer:

mode and midan of data

Step-by-step explanation:

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Answer 2

Concept:-

The number of cricket matches and runs scored in it are given, so we are asked to find the mean, mode and median of the data. And we have to also state that whether they all are same or not.

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

★ Mean

To find mean, Using this formula,

${\sf { \blue{ \boxed{ \sf mean = \frac{sum \: of \: all \: observations }{number \: of \: observations}}}}}$

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Where,

• Number of matches = 11

• Runs scored by a circket team in 11 matches = 90, 40, 30, 110, 80, 20, 30, 15, 30, 10, 8

On substituting the Values,

$\begin{gathered}\\\;\sf{:\rightarrow\;mean\;=\;\bf{{ \frac{90 + 40 + 30 + 110 + 80 + 20 + 30 + 15 + 30 + 10 + 8 }{11} }\:}}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;mean\;=\;\bf{{ \frac{463}{11} }\:}}\end{gathered}$

$\: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;mean\;=\;\bf{{ {42.09} }\:}}\end{gathered}$

∴ Mean = 42.09

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★ Median:-

To find median we will be arranging the numbers in ascending order,

We get,

8, 10, 15, 20, 30, 30, 30, 40, 80, 90, 110.

Number of terms, (n) = 11 (odd)

We know if n is odd we use this formula

${\sf { \blue{ \boxed{ \sf median = \frac{n + 1^{th} }{2} \: term}}}}$

On substituting the Values we get

$\begin{gathered}\\\;\sf{:\rightarrow\;\;median\;=\;\bf{\dfrac{11 + 1}{2} \: term\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;median\;=\;\bf{(\dfrac{12}{2})^{th} \: term\:}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;median\;=\;\bf{6 ^{th} \: term }}\end{gathered}$

• Since, the 6th term is 30.

$\begin{gathered}\\\;\sf{:\rightarrow\;\;median\;=\;\bf{30}}\end{gathered}$

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★ Mode:-

Mode is the value of the Observation for which the frequency is maximum. In other words the observation which occurs maximum times is called mode.

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Therefore,

${\sf { \blue{ \boxed{ \sf mode = most \: occuring \: observation}}}}$

• Since, the value of 30 is repeating maximum number of times i.e., 3.

Therefore,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;mode\;=\;\bf{30}}\end{gathered}$

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★ Now we have;

• Mean = 42.09
• Median = 15
• Mode = 15

We are asked to find whether they all are same or not.

As, we can see only two of them are same.

∴ They are not same.