Question

find the value of q when mean is 47​

Answer 1

hi hay hello answer is 1/14 sorry am not sure ok...

Answer 2

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

Basic Concept :-

There are three methods to find the mean :-

• 1. Direct Method

• 2. Short Cut Method

• 3. Step Deviation Method

Here,

• We prefer step - deviation method as height of the interval is same and calculations become more easier.

Let's solve the problem now!!

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c|c|c}\sf Class\: interval&\sf Frequency\: (f_i)&\sf \: midvalue \: (x_i)&\sf \: u_i&\sf \: f_iu_i\\\frac{\qquad  \qquad}{}&\frac{\qquad  \qquad}{}\\\sf 0 - 20&\sf 8&\sf10&\sf - 2&\sf - 16\\\\\sf 20 - 40 &\sf 15&\sf30&\sf - 1&\sf - 15\\\\\sf 40-60 &\sf 20&\sf50 -A &\sf0&\sf0\\\\\sf 60 - 80&\sf q&\sf70&\sf1&\sf \: q\\\\\sf 80-100&\sf 5&\sf90&\sf2&\sf10\\\sf \\\frac{\qquad}{}&\frac{\qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

Now,

• we have the values

$\rm :\longmapsto\: \sum \: f_i = 48 + q$

$\rm :\longmapsto\:A \: = \: 50$

$\rm :\longmapsto\:h \: = \: 20$

$\rm :\longmapsto\: \sum \: f_iu_i \: = \: - 21 + q$

$\rm :\longmapsto\: \overline{x} \: = \: 47$

Now,

• On substituting all the above values in the formula,

$\rm :\longmapsto\: \overline{x} = A + h \times \dfrac{ \sum \: f_i \: u_i}{ \sum \: f_i}$

$\rm :\longmapsto\:47 = 50 + 20 \times \dfrac{q - 21}{48 + q}$

$\rm :\longmapsto\: - 3 = \dfrac{20q - 420}{48 + q}$

$\rm :\longmapsto\: - 144 - 3q = 20q - 420$

$\rm :\longmapsto\:23q = 276$

$\bf\implies \:q \: = \: 12$

Additional Information :-

1. Mean using Direct Method :-

$\dashrightarrow\sf Mean \: \: \overline{x} = \dfrac{ \sum f_i x_i}{ \sum f_i}$

2. Mean using Short Cut Method :-

$\rm :\longmapsto\: \overline{x} = A + \dfrac{ \sum \: f_i \: d_i}{ \sum \: f_i}$