Question

The mean of given data is 26.

C.I.	0 - 20	20 - 40	40 - 60
f	20	x	10

Statement (1): x = 26.

Statement (2): \[26=\frac{10 \times 20+30 \times x+50 \times 10}{30+x}\]

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation:

Given:

C.I.	f	x(Midpoint) = (Lower limit + upper limit)/2
0-20	20	10
20-40	x	30
40-60	10	50

By formula; \[\text{Mean} = \frac{\Sigma f.x}{\Sigma f}\]

Substituting the values, we get

\[\Rightarrow 26 = \frac{20 \times 10 + x \times 30 + 10 \times 50}{x + 30}\]

So, statement 2 is true.

\[\Rightarrow 26 = \frac{200 + 30x + 500}{30 + x}\]

\[\Rightarrow 26(30 + x) = 200 + 30x + 500\]

\[\Rightarrow 780 + 26x = 700 + 30x\]

\[\Rightarrow 30x - 26x = 780 - 700\]

\[\Rightarrow 4x = 80\]

\[\Rightarrow x = \frac{80}{4}\]

\[\Rightarrow x = 20\]

∴ Statement 1 is false, and statement 2 is true.