SD from numbers 1, 4, 5, 7, 8 is 2.45 . If 10 is added to each then SD will be:

Option d: Will not change. Solution: Concept: Standard Deviation is independent of a change of origin (i.e., adding or subtracting a constant from all observations). Reason: When a constant c is added to every observation, the new observation xi' = xi + c . The new mean x' = x + c . The deviation from the new mean: xi' - x' = (xi + c) - (x + c) = xi - x The deviations remain unchanged, hence the Standard Deviation remains unchanged. Given: SD of 1, 4, 5, 7, 8 = 2.45. When 10 is added to each observation, the new data set is 11, 14, 15, 17, 18 . The SD of the new data set = SD of original data set = 2.45 (unchanged). Hence, Option D is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Nov. 19Question 3129 of 473

All Questions

SD from numbers $\displaystyle 1, 4, 5, 7, 8$ is $\displaystyle 2.45$ . If $\displaystyle 10$ is added to each then SD will be:

Options

\displaystyle 12.45

\displaystyle 24.5

\displaystyle 12

DWill not change

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Correct Answer

✅ Option d — Will not change

All Options:

A $\displaystyle 12.45$
B $\displaystyle 24.5$
C $\displaystyle 12$
DWill not change

Detailed Solution & Explanation

**Concept:** Standard Deviation is independent of a change of origin (i.e., adding or subtracting a constant from all observations). **Reason:** When a constant

\displaystyle c

is added to every observation, the new observation

\displaystyle x_i' = x_i + c

. The new mean

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

. The deviation from the new mean:

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

The deviations remain unchanged, hence the Standard Deviation remains unchanged. **Given:** SD of

\displaystyle \{1, 4, 5, 7, 8\}

= 2.45. When 10 is added to each observation, the new data set is

\displaystyle \{11, 14, 15, 17, 18\}

. The SD of the new data set = SD of original data set = **2.45** (unchanged). Hence, **Option D** 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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SD from numbers 1,4,5,7,8\displaystyle 1, 4, 5, 7, 81,4,5,7,8 is 2.45\displaystyle 2.452.45. If 10\displaystyle 1010 is added to each then SD will be: