Question

THE mean of the given data is 24. find the missing two numbers , if both numbers are same 21, 25, 11, 10, x, 32, 43, 12, 8, 38, y
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Answer 1

Given that,

• The Given Observation;

21, 25, 11, 10, x, 32, 43, 12, 8, 38, y

• The mean of given observation is 24.

• The both variables have same values.

.

To Find,

• The value of 'x' and 'y'.

.

Solution,

As given,

• x = y •••[1]

The Given Observation;

• 21, 25, 11, 10, x, 32, 43, 12, 8, 38, y

Here, The Mean = 24

And, The Sum of observation is 200 + x + y.

As we know,

• $\boxed{ \bar{ x } = \frac{\Sigma f x }{\Sigma f}}$

We found,

$:\longrightarrow 24 = \frac{\Sigma f x }{11}\\ \\ :\longrightarrow 24 = \frac{200 + x + y}{11} \\ \\ :\longrightarrow 264 = 200 + y + y \: \: \: \: \: \: \: \: ...\text{(By Eq [1])}\\ \\ :\longrightarrow 2y = 264 - 200 \\ \\ :\longrightarrow 2y = 64 \\ \\ :\longrightarrow y = 32$

By Equation [1],

• •➤ x = y •••[1]
• •➤ x = 32

Hence, The value of 'x' and 'y'are 32 and 32 respectively.

.

Required Answer,

• The value of 'x' and 'y'are 32 and 32 respectively.