Question

please answer this question​

Answer 1

$\bigstar \purple {\underline{ \pmb{ \bf required \: answer }}} \bigstar$

❍ We are going to use direct method for the sake of simplicity and to avoid complications.

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Formula for Direct method is as follows:-

$\rightarrow \underline{ \boxed{ \pink{{ \frak{mean = \dfrac{Σfixi}{Σfi}}}}}} \bigstar$

• (fi) symbolises frequency
• (xi) symbolises class mark which is calculated as:-

$\rightarrow \underline{ \boxed{ \pink{{ \frak{class \: mark = \dfrac{upper \: limit + lower \: limit}{2}}}}}} \bigstar$

• Σ is the symbol of summation which means sum.
• Σfi is the sum of all the entire frequency
• Σfixi is the addition of fixi category which involves addition of class mark and frequency

Now, The required table is as follows:-

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{cccc}\sf \pink{ literacy \: rate} &\sf \purple{frequency_{(fi)}} &\sf \red{class \: mark_{\:(xi)}} &\sf \blue{fixi}\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 45 - 55 &\sf 4&\sf 50&\sf 200 \\ \\\sf 55 - 65 &\sf 11&\sf 60&\sf 660\\\\\sf 65 - 75 &\sf 12&\sf 70&\sf 840\\\\\sf 75 - 85&\sf 9&\sf 80&\sf 720 \\\\\sf 85 - 95 \: &\sf 4 \: &\sf 40 \: &\sf 360\\\\\sf &\sf Σfi = 40 &\sf & \sf Σfixi =2780 \end{array}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\: \: \: \: \: \: \: \: \dag \underline \frak{substituting \: the \: required \: value \: in \: the \: formula : - }$

$: \implies \sf mean = \dfrac{278 0}{40}$

$: \implies \sf mean = \dfrac{278 \cancel0}{4 \cancel0}$

$: \implies {\boxed{ \pink{ {\frak{ mean = 69.5\%}}}}} \bigstar$

$\therefore \underline{ \sf 69.5\% \: is \: our \: required \: answer}$

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Answer 2

Given :-

A data which shows the literacy rate of 40 cities .

To Find :-

The mean of the following data .

Used Concepts :-

• In the questions , based on mean . We have to take a suitable method but which . It has a rule that if the frequencies are very less in number , So we have to take direct If there are higher frequencies so either step deviation or assumed mean method .
• In board exams you have to do questions according to question . Eg :- If there is very high frequencies in a given data but it is given to you to do by direct method . So , you have to do with direct method .
• Direct method is Σfi.xi/Σfi .
• The symbol of summation ( Σ ) is also known as sigma .

Solution :-

For The Table of the data , Kindly see the attachment .

It is clear from the table that. ,

Σfi = 40 , Σfi.xi = 2780

Let mean of the data = x

Now , By direct Method ,

x = Σfi.xi/Σfi

x = 2780/40

x = 139/2

x = 69.5% .

Hence , the required answer is 69.5% .