If mean of 5 observations x+1, x+3, x+5, x+7 and x+9 is given 15, then the value of x will be:

Option a: 10. Solution: Step 1: Compute the mean of the 5 observations. text{Mean} = (x+1)+(x+3)+(x+5)+(x+7)+(x+9)/5 = 5x + (1+3+5+7+9)/5 = 5x + 25/5 = x + 5 Step 2: Set equal to 15 and solve. x + 5 = 15 implies x = 10 Hence, Option A is the correct answer.

Central Tendency & DispersionPYQ Dec 23Question 2875 of 473

All Questions

If mean of 5 observations $\displaystyle x+1, x+3, x+5, x+7$ and $\displaystyle x+9$ is given 15, then the value of $\displaystyle x$ will be:

Options

\displaystyle 10

\displaystyle 12

\displaystyle 8

\displaystyle 11

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Correct Answer

✅ Option a — $\displaystyle 10$

All Options:

A $\displaystyle 10$
B $\displaystyle 12$
C $\displaystyle 8$
D $\displaystyle 11$

Detailed Solution & Explanation

**Step 1: Compute the mean of the 5 observations.**

\text{Mean} = \frac{(x+1)+(x+3)+(x+5)+(x+7)+(x+9)}{5}

= \frac{5x + (1+3+5+7+9)}{5} = \frac{5x + 25}{5} = x + 5

**Step 2: Set equal to 15 and solve.**

x + 5 = 15 \implies x = 10

Hence, **Option A** is the correct answer.

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If mean of 5 observations x+1,x+3,x+5,x+7\displaystyle x+1, x+3, x+5, x+7x+1,x+3,x+5,x+7 and x+9\displaystyle x+9x+9 is given 15, then the value of x\displaystyle xx will be: