Measures of Central Tendency and DispersionMCQMTP June 2023 Series IIQuestion 2917 of 473

The average of ' $\displaystyle r$ ' consecutive numbers starting from $\displaystyle 1$ is ' $\displaystyle r$ '. If $\displaystyle 2$ is added to each of the number. Then the new average will be?

Options

\displaystyle r+s

\displaystyle r+(s/2)

\displaystyle r

DNone of these

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Correct Answer

✅ Option a — $\displaystyle r+s$

All Options:

A $\displaystyle r+s$
B $\displaystyle r+(s/2)$
C $\displaystyle r$
DNone of these

Detailed Solution & Explanation

**Step 1: Clarify the question.** The question says the average of

\displaystyle r

consecutive numbers starting from 1 is

\displaystyle r

. The average of first

\displaystyle r

natural numbers (1, 2, ...,

\displaystyle r

) is:

\bar{x} = \frac{r+1}{2}

For this to equal

\displaystyle r

\displaystyle \frac{r+1}{2} = r \Rightarrow r+1 = 2r \Rightarrow r = 1

. This only works for

\displaystyle r=1

. The question may be using a different statement — that the current average is some value. **Step 2: Effect of adding 2 to each number.** If each number has 2 added to it, the new average

\displaystyle =

old average

\displaystyle + 2

. If old average

\displaystyle = r

, new average

\displaystyle = r + 2

. This is "None of these" if options don't include

\displaystyle r+2

, or Option A if

\displaystyle s = 2

(which seems to be the case based on context —

\displaystyle s

likely represents the constant added, which is 2). With

\displaystyle s=2

, Option A gives

\displaystyle r + s = r + 2

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

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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The average of 'r\displaystyle rr' consecutive numbers starting from 1\displaystyle 11 is 'r\displaystyle rr'. If 2\displaystyle 22 is added to each of the number. Then the new average will be?