Question

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. Number of plants 0­ − 2 2­ − 4 4 − 6 6 − 8 8 − 10 10 − 12 12 − 14 Number of houses 1 2 1 5 6 2 3 Which method did you use for finding the mean, and why?

Answer 1

Solution:

$\begin{tabular}{|l|l|l|l|} \cline{1-4} Class & Freq & (x_i) & x_i f_i \\ \cline{1-4} 0-2 & 1 & 1 & 1 \\ \cline{1-4} 2-4 & 2 & 3 & 6 \\ \cline{1-4} 4-6 & 1 & 5 & 5 \\ \cline{1-4} 6-8 & 5 & 7 & 35 \\ \cline{1-4} 8-10 & 6 & 9 & 54 \\ \cline{1-4} 10-12 & 2 & 11 & 22 \\ \cline{1-4} 12-14 & 3 & 13 & 39 \\ \cline{1-4} Total & 20 & & 162 \\ \cline{1-4} \end{tabular}$

Direct Mean Method:

$\bar x = \frac{ \Sigma \: xifi }{\Sigma \: fi} \\ \\ \bar x = \frac{162}{20} \\ \\ \bar x = 8.1\:plants$

I am using direct mean method because the calculation is simple.

Answer 2

$\: \: \: \: \: \: \: \: \: \huge\colorbox{lightgreen}{\tt{Answer ♥︎}}$

Let us find class marks ( xi ) for each interval by using the relation :

${\boxed{\sf{\pink{Class \: mark \: ( xi ) = \frac{Upper \: class \: limit + Lower \: class \: limit}{2} }}}}$

Now, we may compute ( xi ) and ( fixi ) as given in above picture...

From the table, we may observe that :

${\boxed{\sf{\pink{Mean \: ( Xᷓ ) = \frac{∑fixi}{∑fi} }}}}$

$\sf{Mean \: ( Xᷓ ) = \frac{162}{20} }$

${\underline{\underline{\sf{\bold{\purple{∴Mean ( Xᷓ ) = 8.1}}}}}}$

So, mean number of plants per house is 8.1

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