Question

If ∑ = 15, ∑ = 3 + 36 and mean of any distribution is 3, then p = ___​

Answer 1

Appropriate Question :-

If ∑f = 15, ∑fx = 3p + 36 and mean of distribution is 3, then p = ___

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

Given that,

$\sf \: \sum \: f \: = \: 15$

and

$\sf \: \sum \: fx \: = \: 3p + 36$

and

$\sf \: \overline{x} \: = \: 3$

We know,

Mean using Direct Method is given by

$\bf \: \overline{x} \: = \: \frac{ \sum \: fx}{ \sum \: f}$

So, on substituting the values, we get

$\sf \: 3 = \dfrac{3p + 36}{15}$

$\sf \: 3p + 36 = 45$

$\sf \: 3p = 45 - 36$

$\sf \: 3p = 9$

$\bf\implies \:p = 3$

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Additional Information

1. Mode of the continuous series is given by

$\red{\boxed{ \boxed{\sf{Mode = l + \bigg(\dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \bigg) \times h }}}}$

where,

l is lower limit of modal class.

$\sf{f_1}$ is frequency of modal class

$\sf{f_0}$ is frequency of class preceding modal class

$\sf{f_2}$ is frequency of class succeeding modal class

h is class height.

2. Mean using Short Cut Method

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

3. Mean using Step Deviation Method

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