Measures of Central Tendency and DispersionMCQPYQ June 24 Series IQuestion 2937 of 473
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The mean of first 3 terms is 14 and the mean of next 2 terms is 18. The mean of 5 numbers is -

Options

A14.5
B15
C14
D15.6
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Correct Answer

✅ Option d — 15.6

All Options:

  • A14.5
  • B15
  • C14
  • D15.6

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Detailed Solution & Explanation

We are given: - Number of observations in the first group: n1=3\displaystyle n_1 = 3 - Mean of the first group: xˉ1=14\displaystyle \bar{x}_1 = 14 - Sum of observations of the first group: Sum1=3×14=42\displaystyle \text{Sum}_1 = 3 \times 14 = 42 - Number of observations in the second group: n2=2\displaystyle n_2 = 2 - Mean of the second group: xˉ2=18\displaystyle \bar{x}_2 = 18 - Sum of observations of the second group: Sum2=2×18=36\displaystyle \text{Sum}_2 = 2 \times 18 = 36 - Total number of observations: n=n1+n2=3+2=5\displaystyle n = n_1 + n_2 = 3 + 2 = 5 - Combined sum of all 5 observations: Sumtotal=42+36=78\displaystyle \text{Sum}_{\text{total}} = 42 + 36 = 78 Using the formula for the combined mean: xˉ=Sumtotaln=785=15.6\bar{x} = \frac{\text{Sum}_{\text{total}}}{n} = \frac{78}{5} = 15.6 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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