When 10 is subtracted from all the observations, the mean is reduced to 60% of its value. If 5 is added to all the observations, then the mean will be

Option b: 30. Solution: Step 1: Set up equation for first condition. Let original mean = x . When 10 is subtracted from all observations: x - 10 = 0.6x 0.4x = 10 x = 25 Step 2: Compute the new mean when 5 is added. New mean = x + 5 = 25 + 5 = 30 Note: The computed new mean is 30 (Option B), not 65 (Option D). Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IQuestion 2930 of 473

All Questions

When $\displaystyle 10$ is subtracted from all the observations, the mean is reduced to $\displaystyle 60\%$ of its value. If $\displaystyle 5$ is added to all the observations, then the mean will be

Options

A25

B30

C60

D65

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Correct Answer

✅ Option b — 30

All Options:

Detailed Solution & Explanation

**Step 1: Set up equation for first condition.** Let original mean

\displaystyle = \bar{x}

. When 10 is subtracted from all observations:

\bar{x} - 10 = 0.6\bar{x}

0.4\bar{x} = 10

\bar{x} = 25

**Step 2: Compute the new mean when 5 is added.**

\text{New mean} = \bar{x} + 5 = 25 + 5 = 30

**Note:** The computed new mean is **30** (Option B), not 65 (Option D). Hence, **Option B** 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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When 10\displaystyle 1010 is subtracted from all the observations, the mean is reduced to 60%\displaystyle 60\%60% of its value. If 5\displaystyle 55 is added to all the observations, then the mean will be