Question

If Σfi = 13, Σfixi = 3p + 70 and the mean of any distribution is 7, then the value of p is:


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Answer 1

Answer:

The value of p is 7.

Step-by-step-explanation:

We have given that,

• Sum of frequencies $\displaystyle{\sf\:(\:\Sigma\:f_i\:)\:=\:13}$

• $\displaystyle{\sf\:\Sigma\:x_i\:f_i\:=\:3p\:+\:70}$

• Mean of the distribution = 7

We have to find the value of p.

We know that,

$\displaystyle{\pink{\sf\:Mean\:=\:\dfrac{\sum\:x_i\:f_i}{\sum\:f_i}}}$

$\displaystyle{\implies\sf\:7\:=\:\dfrac{3p\:+\:70}{13}}$

$\displaystyle{\implies\sf\:3p\:+\:70\:=\:13\:\times\:7}$

$\displaystyle{\implies\sf\:3p\:+\:70\:=\:91}$

$\displaystyle{\implies\sf\:3p\:=\:91\:-\:70}$

$\displaystyle{\implies\sf\:3p\:=\:21}$

$\displaystyle{\implies\sf\:p\:=\:\cancel{\dfrac{21}{3}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:p\:=\:7}}}}$

∴ The value of p is 7.

Answer 2

Question:-

• If Σfi = 13, Σfixi = 3p + 70 and the mean of any distribution is 7, then the value of p is:

To Find:-

• Find the value of p.

Solution:-

Given ,

• Σfi = 13

• Σfixi = 3p + 70

• Mean of distribution = 7

According to the Question:-

$\dashrightarrow\sf \: Mean = \dfrac { Σ x_i f_i } { Σf_i }$

$\dashrightarrow\sf \: 7 = \dfrac { 3p + 70 } { 13 }$

$\dashrightarrow\sf \: 3p + 70 = 7 \times 13$

$\dashrightarrow\sf \: 3p + 70 = 91$

$\dashrightarrow\sf \: 3p = 91 - 70$

$\dashrightarrow\sf \: 3p = 21$

$\dashrightarrow\sf \: p = \dfrac { 21 } { 3 }$

$\displaystyle{\implies{\boxed{\redΣfi = 13{\sf\:p\:=\:7}}}}$