Measures of Central Tendency and DispersionMCQPYQ Nov 18Question 2856 of 473
All Questions

The mean of 20 items of a data is 5 & if each item is multiplied by 3, then the new mean will be

Select Your Answer (Keyboard: A, B, C, D)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $15$

All Options:

  • A5\displaystyle 5
  • B$10$
  • C$15$
  • D$20$

Detailed Solution & Explanation

**Step 1: State the given information.** Number of items n=20\displaystyle n = 20, Original mean xˉ=5\displaystyle xˉ=5\displaystyle \bar{x} = 5. **Step 2: Apply the property of mean under multiplication.** If each item xi\displaystyle x_i is multiplied by a constant k\displaystyle k, the new mean becomes k⋅xˉ\displaystyle k ⋅\displaystyle \cdot xˉ\displaystyle \bar{x}. Here k=3\displaystyle k = 3, so: New mean=3×xˉ=3×5=15New mean=3\displaystyle \text{New mean} = 3 ×\displaystyle \times xˉ=3\displaystyle \bar{x} = 3 ×\displaystyle \times 5 = 15 **Step 3: Verification.** Original sum =n×xˉ=20×5=100\displaystyle = n ×\displaystyle \times xˉ=20\displaystyle \bar{x} = 20 ×\displaystyle \times 5 = 100. New sum =3×100=300\displaystyle = 3 ×\displaystyle \times 100 = 300. New mean =30020=15\displaystyle = 30020=15\displaystyle \frac{300}{20} = 15. ✓ 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.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

More Questions from Measures of Central Tendency and Dispersion

If the range of $28, 22, 40, 20, 15, 50$ is

If the S.D. of the 1st\displaystyle 1^{st} n\displaystyle n natural numbers is 30\displaystyle 30\displaystyle \sqrt{30} then the value of n\displaystyle n is

If the variance of $5, 7, 9\displaystyle and $11 is 4\displaystyle 4, then the coefficient of variation is:

A helicopter flies from A to B at the rate of 500 km/hr. and comes back at the rate 700 km/hr. The average speed of the helicopter is

If Arithmetic Mean (A.M.) and Geometric Mean (G.M.) of two numbers are 6.50 and 6 respectively, then the two numbers are

Which of the following is not a method of dispersion?

Ready to Master Measures of Central Tendency and Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free