Mean and S.D. of a given set of observations is $1,500 and $400 respectively. If there is an increment of $100 in the first year and each observation is hiked by $20% in 2 nd years, then find new mean and S.D.

Option a: $1920, 480$. Solution: Given: Original Mean = 1500, Original SD = 400 Year 1: Increment of 100 (add 100 to each observation). - New Mean = $1500 + 100 = 1600$ - New SD = $400$ (unchanged, since adding a constant doesn't affect SD) Year 2: 20% hike (multiply each observation by 1.20). - New Mean = $1600 × 1.20 = 1920$ - New SD = $400 × 1.20 = 480$ (SD scales proportionally) Final: Mean = 1920, SD = 480 (Option A). The given correctoption 'd' ($1600, 400$) represents only after Year 1, not after Year 2. After BOTH transformations: Mean = 1920, SD = 480. Hence, Option A is the correct answer.

Mean and S.D. of a given set of observations is $1,500 and $400 respectively. If there is an increment of $100 in the first year and each observation is hiked by $20% in 2 nd years, then find new mean and S.D.

The correct answer is Option a: $1920, 480$. Given: Original Mean = 1500, Original SD = 400 Year 1: Increment of 100 (add 100 to each observation). - New Mean = $1500 + 100 = 1600$ - New SD = $400$ (unchanged, since adding a constant doesn't affect SD) Year 2: 20% hike (multiply each observation by 1.20). - New Mean = $1600 × 1.20 = 1920$ - New SD = $400 × 1.20 = 480$ (SD scales proportionally) Final: Mean = 1920, SD = 480 (Option A). The given correctoption 'd' ($1600, 400$) represents only after Year 1, not after Year 2. After BOTH transformations: Mean = 1920, SD = 480. Hence, Option A is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series IIQuestion 3204 of 473

All Questions

Mean and S.D. of a given set of observations is $1,500 $\displaystyle and $400$ respectively. If there is an increment of $100 $\displaystyle in the first year and each observation is hiked by $20\%$ in $\displaystyle 2$ nd years, then find new mean and S.D.

Select Your Answer (Keyboard: A, B, C, D)

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Correct Answer

✅ Option a — $1920, 480$

All Options:

A$1920, 480$
B$1920, 580$
C$1600, 480$
D$1600, 400$

Detailed Solution & Explanation

**Given:** Original Mean = 1500, Original SD = 400 **Year 1: Increment of 100 (add 100 to each observation).** - New Mean = $1500 + 100 = 1600$ - New SD = $400$ (unchanged, since adding a constant doesn't affect SD) **Year 2: 20% hike (multiply each observation by 1.20).** - New Mean = $1600

\displaystyle \times

1.20 = 1920$ - New SD = $400

\displaystyle \times

1.20 = 480$ (SD scales proportionally) **Final: Mean = 1920, SD = 480** (Option A). The given `correct_option` 'd' ($1600, 400$) represents only after Year 1, not after Year 2. After BOTH transformations: Mean = 1920, SD = 480. 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.

Key Concepts to Understand

Set

A well-defined collection of distinct objects (called elements or members). Sets are denoted by capital letters and elements are listed within curly braces. Key operations include Union (∪), Intersection (∩), and Complement.

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Mean and S.D. of a given set of observations is $1,500\displaystyle and &#36;400 respectively. If there is an increment of $100\displaystyle in the first year and each observation is hiked by &#36;20\% in 2\displaystyle 22nd years, then find new mean and S.D.