Question

5. The mean of the following data is
x 5 10 15 20 25 30
f 4 5 3 2 3 3


(a) 15
(b) 16
(c) 17
(d) none of these


please tell me the answer​

Answer 1

$\large\underline{\sf{Solution-}}$

The frequency distribution table is as

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c}\sf x&\sf \: f&\sf \:fx\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}\\\sf 5&\sf 4&\sf20\\\\\sf 10&\sf 5&\sf50\\\\\sf 15 &\sf 3&\sf45\\\\\sf 20&\sf 2&\sf40 \\\\\sf 25&\sf 3&\sf75 \\\\\sf 30&\sf 3&\sf90\\\frac{\qquad}{}&\frac{\qquad}{}&\frac{\qquad \qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

So, we get

$\rm :\longmapsto\: \sum \: fx \: = \: 320$

$\rm :\longmapsto\: \sum \: f \: = \: 20$

We know,

➢ Mean using Direct Method is given by

$\purple{\rm :\longmapsto\:\boxed{\tt{ Mean \: = \: \frac{ \sum \: fx}{ \sum \: f} \: }}}$

So, on substituting the values, we get

$\rm :\longmapsto\:Mean = \dfrac{320}{20}$

$\rm\implies \:\boxed{\tt{ \: \: Mean \: = \: 16 \: \: }}$

Hence, Option (b) is correct

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MORE TO KNOW

1. Mean using Short Cut Method is given by

$\purple{\rm :\longmapsto\:\boxed{\tt{ Mean \: = \: A + \frac{ \sum \: fd}{ \sum \: f} \: where \: d = x - A}}}$

2. Mean using Step Deviation Method is given by

$\purple{\rm :\longmapsto\:\boxed{\tt{ Mean \: = \: A + h\frac{ \sum \: fu}{ \sum \: f} \: where \: u= \frac{x - A}{h} }}}$