Question

If the mean of the following distribution is 6, find the value of p.

2 4 6 10 P+5

3 2 3 2​

Answer 1

Answer:

the answer is 668 ok broo it is a correct answer

Answer 2

Question :

If the Mean of the following distribution is 6, find the Value of p.

$\begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} x_i & 2 & 4& 6 & 10 & p+5\\\cline{1-6} f_i & 3 & 2 & 3 & 1 & 2\\\cline{1-6}\end {tabular}$

$\begin {gathered} \end {gathered}$

Solution :

We may prepare the Frequency table as given below:

$\begin{tabular}{|c|c|c|}\cline{1-3} x_i & f_i & (x_i \times f_i)\\\cline{1-3} 2 & 3& 6\\\cline{1-3} 4& 2& 8\\\cline{1-3} 6 & 3 & 18\\\cline{1-3} 10 & 1 & 10\\\cline{1-3}p + 5 & 2 & 2p+10\\\cline{1-3} & \sum f_i = 11 & \sum (x_i \times f_i) = 2p + 52\\\cline{1-3} \end{tabular}$

$\therefore \ \mathtt {Mean = \dfrac{\sum (x_i \times f_i)}{\sum f_i}} = \bold {\dfrac{2p+52}{11}}$

But, Mean = 6 (given)

$\begin {gathered} \end {gathered}$

$\begin{aligned} \therefore \ \dfrac{2p+52}{11} = 6 &\Rightarrow 2p+52 = 6 \times 11\\\\&\Rightarrow 2p+52 = 66\\\\&\Rightarrow \bold {2p = 14} \ \ \boxed{\because 66 - 52 = 14}\\\\&\Rightarrow \bold p = \dfrac{14}{2} = \underline{\underline{\bold 7}} \end{aligned}$

Hence, p = 7

$\begin {gathered} \end {gathered}$

More Information about Mean :

The Average of a given set of Numbers is called the Arithmetic Mean, or simply the Mean, of the given Numbers.

$\mathtt{Mean = \dfrac{Sum\: of\: Observations}{Number\: of\: Observations}}$

$\begin {gathered} \end {gathered}$

The Mean of n Observations x₁, x₂, . . ., $x_n$ is given by -

$\mathrm {\bar {x} = \dfrac{(x_1 + x_2 + ... + x_n)}{n}}$