Question 3Find the mean age of 100 residents of a town from the following data- - - - - - - 0 10 20 30 40 50 60 70- - - - 100 90 75 50 25 15 5 0- -

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Standard VIII

Mathematics

Finding Mean for Grouped Data When Class Intervals Are Given

Question 3Fin...

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Question 3
Find the mean age of 100 residents of a town from the following data.
$\begin{matrix} A g e e q u a l a n d a b o v e (i n y e a r s) & 0 & 10 & 20 & 30 & 40 & 50 & 60 & 70 N u m b e r o f p e r s o n s & 100 & 90 & 75 & 50 & 25 & 15 & 5 & 0 \end{matrix}$

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Solution

Here, we observe that all 100 residents of a town have age equal and above 0. Since 90 residents of a town have age equal and above 10.
So, 100-90=10 residents lies in the interval 0-10 and so on. Continue in this manner, we get frequency of all class intervals. Now, we construct the frequency distribution table.
$\begin{matrix} C l a s s i n t e r v a l & N u m b e r o f p e r s o n s (f_{i}) & C l a s s m a r k s & u_{i} = \frac{x_{i} - a}{h} & f_{i} u_{i} 0 - 10 & 100 - 90 = 10 & 5 & - 3 & - 30 10 - 10 & 90 - 75 = 15 & 15 & - 2 & - 30 20 - 30 & 75 - 50 = 25 & 25 & - 1 & - 25 30 - 40 & 50 - 25 = 25 & 35 = a & 0 & 0 40 - 50 & 25 - 15 = 10 & 45 & 1 & 10 50 - 60 & 15 - 5 = 10 & 55 & 2 & 20 60 - 70 & 5 - 0 = 5 & 5 & 3 & 15 N = \sum f_{i} = 100 & \sum f_{i} u_{i} = - 40 \end{matrix}$
Here, (assumed mean) a=35
and (class width) h=10
By step deviation method,
Mean $(¯ x) = a + \frac{\sum f_{i} u_{i}}{\sum f_{i}} \times h = 35 + \frac{(- 40)}{100} \times 10 = 35 - 4 = 31$
Hence, the required mean age is 31 years.

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Question 3 Find the mean age of 100 residents of a town from the following data. Age equal and above (in years)010203040506070Number of persons100907550251550

Question 3
Find the mean age of 100 residents of a town from the following data.
$\begin{matrix} A g e e q u a l a n d a b o v e (i n y e a r s) & 0 & 10 & 20 & 30 & 40 & 50 & 60 & 70 N u m b e r o f p e r s o n s & 100 & 90 & 75 & 50 & 25 & 15 & 5 & 0 \end{matrix}$