Question

Please solve this.
Answer only moderators please no one else.​

Answer 1

Answer:

the missing frequencies are 4 and 25.

Step-by-step explanation:

the final result is f1 and de value that i have assumed ..

please go through the steps

Answer 2

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

Let assume that the two missing frequencies be a and b.

So, frequency distribution table for calculations of mean are as follow :

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c}\sf x&\sf \: f&\sf \:fx\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}\\\sf 0&\sf 2&\sf0\\\\\sf 1&\sf 8&\sf8\\\\\sf 2 &\sf 13&\sf26\\\\\sf 3&\sf a&\sf3a \\\\\sf 4&\sf 29&\sf116\\\\\sf 5&\sf b&\sf5b\\\\\sf 6&\sf 10&\sf60\\\\\sf 7&\sf 3&\sf21\\\frac{\qquad}{}&\frac{\qquad}{}&\frac{\qquad \qquad}{}\\\sf & 65 + a + b\sf & 231 + 3a + 5b\end{array}}\end{gathered}\end{gathered}\end{gathered}$

Now, it is given that,

$\rm \: \sum \: f \: = \: 100$

$\rm \: 65 + a + b = \: 100$

$\rm \: a + b = \: 100 - 65$

$\rm \:a + b = 35$

$\rm\implies \:a = 35 - b - - - (1)$

Now, further given that

$\rm \: \overline{x} \: = \: 3.68$

$\rm \: \dfrac{ \sum \: fx}{ \sum \: f} \: = \: 3.68$

$\rm \: \dfrac{231 + 3a + 5b}{100} = 3.68$

$\rm \: 231 + 3a + 5b = 368$

$\rm \: 3a + 5b = 368 - 231$

$\rm \: 3a + 5b = 137$

$\rm \: 3(35 - b) + 5b = 137$

$\rm \: 105 - 3b + 5b = 137$

$\rm \: 2b = 137 - 105$

$\rm \: 2b = 32$

$\rm\implies \:b \: = \: 16$

On substituting b = 16 in equation (1), we get

$\rm \: a = 35 - 16$

$\rm\implies \:a \: = \: 19$

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

Additional Information :-

1. Mean using Direct Method

$\boxed{ \rm{ \:\rm \: \overline{x} \: = \: \dfrac{ \sum \: fx}{ \sum \: f} \: }}$

2. Mean using Short Cut Method

$\boxed{ \rm{ \:\rm \: \overline{x} \: = A \: + \: \dfrac{ \sum \: fd}{ \sum \: f} \: }}$

3. Mean using Step Deviation Method

$\boxed{ \rm{ \:\rm \: \overline{x} \: = A \: + \: \dfrac{ \sum \: fu}{ \sum \: f} \times h \: }}$