Question

If the mean of the data given in adjoining table is 20, the relation between x₁ and x₂ is:

x	f
10	x1
20	20
30	x2

पर्याय

• x₁ + x₂ = 30

• x₁ − x₂ = 15

• x₁ − x₂ = 0

• x₁ + x₂ = 20

Answer 1

x₁ − x₂ = 0

Explanation:

x	f	fx
10	x1	10x1
20	20	400
30	x2	30x2
Total	Σf = 20 + x1 + x2	Σfx = 400 + 10x1 + 30x2

By formula,

\[\text{Mean} = \frac{\Sigma fx}{\Sigma f}\]

Substituting values we get:

\[\Rightarrow 20 = \frac{400 + 10x_1 + 30x_2}{20 + x_1 + x_2}\]

\[\Rightarrow 20(20 + x_1 + x_2) = 400 + 10x_1 + 30x_2\]

\[\Rightarrow 400 + 20x_1 + 20x_2 = 400 + 10x_1 + 30x_2\]

\[\Rightarrow 20x_1 - 10x_1 + 20x_2 - 30x_2 = 400 - 400\]

\[\Rightarrow 10x_1 - 10x_2 = 0\]

\[\Rightarrow 10(x_1 - x_2) = 0\]

\[\Rightarrow x_1 - x_2 = 0.\]