Question

The mean of the following data is 26.5 and the total frequency is 60

class 0-10 10-20 20-30 30-40 40-50
freq 6 x 17 y 8

I want perfect answer

I will mark brainlest​

Answer 1

Question:-

• The mean of the following data is 26.5 and the total frequency is 60. Find the value of x and y

• Data:-

$\boxed{\begin{array}{c|c} \bf{Class - Interval} & \bf{Frequency} \\ \sf{0-10} & \sf{6} \\ \sf{10-20} & \sf{x} \\ \sf{20-30} & \sf{17} \\ \sf{30 - 40} & \sf{y} \\ \sf{40 - 50} & \sf{8} \end{array}}$

Required Solution:-

Let us make the required frequency table first!

$\boxed{\begin{array}{c|c|c|c} \bf{Class - Interval} & \bf{Frequency\:(f_i)} & \bf{Class\:mark\:(x_i)} & \bf{f_i x_i} \\ \cline{1-4} \sf{0-10} & \sf{6} & \sf{5} & \sf{30} \\ \sf{10-20} & \sf{x} & \sf{15} & \sf{15x} \\ \sf{20-30} & \sf{17} & \sf{25} & \sf{425} \\ \sf{30-40} & \sf{y} & \sf{35} & \sf{35y} \\ \sf{40 - 50} & \sf{8} & \sf{45} & \sf{360} \\ \cline{1-4} & \sf{\sum f_i = 31 + x + y} & & \sf{\sum f_i x_i = 815 + 15 x + 35y} \end{array}}$

We already have:-

• Total frequency = 60 --------- (a)
• Mean = 26.5

From the frequency table we also have:-

• Total frequency = 31 + x + y

Hence,

The total frequency is as follows:-

31 + x + y = 60

= x + y = 60 - 31

= x + y = 29

=> x = 29 - y ----------- (i)

Now,

We know:-

• $\dag\boxed{\sf{Mean = \dfrac{\sum f_i x_i}{\sum f_i}}}$

Here,

We will put the value of ∑fᵢ = 60

Hence,

$\sf{26.5 = \dfrac{815 + 15x + 35y}{60}}$

$= \sf{26.5 \times 60 = 815 + 15x + 35y}$

$= \sf{1590 = 815 + 15x + 35y}$

$= \sf{1590 - 815 = 15x + 35y}$

$= \sf{775 = 5(3x + 7y)}$

$= \sf{\dfrac{775}{5} = 3x + 7y}$

$= \sf{155 = 3x + 7y}$

$\implies \sf{3x + 7y = 155 .... (ii)}$

Putting the value of x in equation (ii) from equation (i):-

= 3(29 - y) + 7y = 155

= 87 - 3y + 7y = 155

= 87 + 4y = 155

= 4y = 155 - 87

= 4y = 68

$= \sf{y = \dfrac{68}{4}}$

= y = 17

Now, Putting the value of y in equation (i):-

= x = 29 - 17

= x = 12

∴ The values of x and y are 17 and 12 respectively.

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