If the standard deviation of 1, 2, 3, 4, ..., 10 is sigma , then the SD of 11, 12, 13, 14, ..., 20 is:

Option c: sigma. Solution: Key insight: The series 11, 12, 13, ..., 20 is obtained by adding 10 to each term of 1, 2, 3, ..., 10 . Property: Adding a constant to all observations does NOT change the Standard Deviation. Proof: If xi' = xi + 10 , then x' = x + 10 . xi' - x' = (xi + 10) - (x + 10) = xi - x Deviations are unchanged, hence SD is unchanged. Conclusion: SD of 11, 12, ..., 20 = SD of 1, 2, ..., 10 = sigma Hence, Option C is the correct answer.

If the standard deviation of $1, 2, 3, 4, ..., 10$ is $\sigma$, then the SD of $11, 12, 13, 14, ..., 20$ is:

The correct answer is Option c: $\sigma$. **Key insight:** The series $11, 12, 13, ..., 20$ is obtained by adding 10 to each term of $1, 2, 3, ..., 10$. **Property:** Adding a constant to all observations does NOT change the Standard Deviation. **Proof:** If $x_i' = x_i + 10$, then $\bar{x}' = \bar{x} + 10$. $$x_i' - \bar{x}' = (x_i + 10) - (\bar{x} + 10) = x_i - \bar{x}$$ Deviations are unchanged, hence SD is unchanged. **Conclusion:** SD of $\{11, 12, ..., 20\}$ = SD of $\{1, 2, ..., 10\}$ = $\sigma$ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 22 - Series IQuestion 3188 of 473

All Questions

If the standard deviation of $\displaystyle 1, 2, 3, 4, ..., 10$ is $\displaystyle \sigma$ , then the SD of $\displaystyle 11, 12, 13, 14, ..., 20$ is:

Options

\displaystyle 10\sigma

\displaystyle 10+\sigma

\displaystyle \sigma

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $\displaystyle \sigma$

All Options:

A $\displaystyle 10\sigma$
B $\displaystyle 10+\sigma$
C $\displaystyle \sigma$
DNone of these

Detailed Solution & Explanation

**Key insight:** The series

\displaystyle 11, 12, 13, ..., 20

is obtained by adding 10 to each term of

\displaystyle 1, 2, 3, ..., 10

. **Property:** Adding a constant to all observations does NOT change the Standard Deviation. **Proof:** If

\displaystyle x_i' = x_i + 10

, then

\displaystyle \bar{x}' = \bar{x} + 10

x_i' - \bar{x}' = (x_i + 10) - (\bar{x} + 10) = x_i - \bar{x}

Deviations are unchanged, hence SD is unchanged. **Conclusion:** SD of

\displaystyle \{11, 12, ..., 20\}

= SD of

\displaystyle \{1, 2, ..., 10\}

\displaystyle \sigma

Hence, **Option C** 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.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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If the standard deviation of 1,2,3,4,...,10\displaystyle 1, 2, 3, 4, ..., 101,2,3,4,...,10 is σ\displaystyle \sigmaσ, then the SD of 11,12,13,14,...,20\displaystyle 11, 12, 13, 14, ..., 2011,12,13,14,...,20 is: