Question

(1) The marks obtained by the students in an examination of 400 marks
is given in the following frequency distribution table. Find the mean
of the distribution.
Marks 200-240 240-280 280-320 320-360 360-400
frequency | 10 20 30 24 16​

Answer 1

Answer:118.1

Step-by-step explanation: summisionfi=100

Summision fixing=11810

Therefore,,mean,=summisionfixi/summisionfi

=11810/100

=118.1

Answer 2

$\Large{\underbrace{\underline{\sf{Understanding\: the\: Concept}}}}$

Here, this is a question from statistics, where we have to find the mean of the given distribution table.

We have the formula for mean:

$\displaystyle\sf\;Mean,\:(\overline{X})=\dfrac{\sum X_iF_i}{\sum F_i}$

$\rule{380}{2}$

The required value for formula of mean can be obtained by following table:

$\fbox{\boxed{\begin{array}{c|c|c|c}&&&&\bf{Marks\;}&\bf{Frequency}&\bf{X_1}&\bf{X_iF_i}\\&\sf{(F_i)}&\sf{\dfrac{Upper+lower\: limit}{2}}&&&&\\\cline{1-4}&&&&200-240&10&\dfrac{440}{2}=220&2200&&&&\\\cline{1-4}&&&&240-280&20&\dfrac{520}{2}=260&5200&&&&\\\cline{1-4}&&&&280-320&30&\dfrac{600}{2}=300&900&&&&\\\cline{1-4}&&&&320-360&24&\dfrac{680}{2}=340&3160&&&&\\\cline{1-4}&&&&360-400&16&\dfrac{760}{2}=380&6080&&&&\\\cline{1-4}&&&&\sf{Total}&\sf\sum\;F_i=100&&\sf\sum\;F_i X_i=30,640&&&&\end{array}}}$

$\rule{380}{2}$

From here we have obtained values of:

$:\implies \displaystyle\sf\sum X_iF_i$

$\displaystyle\sf:\implies \sum F_i$

Now put these values in the formula:

$\displaystyle\sf\;Mean,\:(\overline{X})=\dfrac{\sum X_iF_i}{\sum F_i}$

$\sf\;Mean,\:(\overline{X})=\dfrac{30,640}{100}$

$\sf\;Mean,\:(\overline{X})=306.4$

∵ So the required mean is 306.4.

$\rule{380}{2}$

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