Question

Find mean of the above Image​

Answer 1

Answer:

10

Step-by-step explanation:

mean = 12+14+8+6+10/5

= 10

Answer 2

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

The frequency distribution table for calculations of mean using Step Deviation Method is given below :-

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c|c|c}\sf Class\: interval&\sf Frequency\: (f_i)&\sf \: midvalue \: (x_i)&\sf \: u_i&\sf \: f_iu_i\\\frac{\qquad  \qquad}{}&\frac{\qquad  \qquad}{}\\\sf 100 - 120&\sf 12&\sf110&\sf - 2&\sf - 24\\\\\sf 120 - 140 &\sf 14&\sf130&\sf - 1&\sf - 14\\\\\sf 140-160 &\sf 8 &\sf150&\sf0&\sf0\\\\\sf 160 - 180&\sf 6&\sf170&\sf1&\sf6\\\\\sf 180-200&\sf 10&\sf190&\sf2&\sf20\\\frac{\qquad}{}&\frac{\qquad}{}\\\sf & 50\sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

Now, from above calculations, we have

$\rm \: \: \: \: \bull \: \: \: \: A = 150$

$\rm \: \: \: \: \bull \: \: \: \: h = 20$

$\rm \: \: \: \: \bull \: \: \: \: \sum \: f_i = 50$

$\rm \: \: \: \: \bull \: \: \: \: \sum \: f_i u_i= - 12$

We know, Mean using Step Deviation Method is given by

$\boxed{ \rm{ \:\bf \: Mean = A \: + \: \dfrac{ \sum \: f_iu_i}{ \sum \: f_i} \times h \: \: }}$

So, on substituting the values, we get

$\rm \: Mean = 150 \: + \: \dfrac{ - 12}{50} \times 20$

$\rm \: Mean = 150 \: - \: \dfrac{ 12}{5} \times 2$

$\rm \: Mean = 150 \: - \: \dfrac{24}{5}$

$\rm \: Mean = 150 \: - \: 4.8$

$\rm\implies \:\boxed{ \rm{ \:\rm \: Mean = 145.2 \: \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

1. Mean using Direct Method

$\boxed{ \rm{ \:\bf \: Mean = \: \dfrac{ \sum \: f_ix_i}{ \sum \: f_i}\: \: }}$

2. Mean using Short Cut Method

$\boxed{ \rm{ \:\bf \: Mean = A \: + \: \dfrac{ \sum \: f_id_i}{ \sum \: f_i}\: \: }}$