The median of the observations 42, 72, 35, 92, 67, 85, 72, 81, 51, 56 is

Option a: 69.5. Solution: We are given the observations: 42, 72, 35, 92, 67, 85, 72, 81, 51, 56 . 1. Arrange the data in ascending order: 35, 42, 51, 56, 67, 72, 72, 81, 85, 92 Here, the number of observations is n = 10 . 2. The median is the average of the two middle-most observations (the 5th and 6th observations): - 5th observation: 67 - 6th observation: 72 3. Calculate the median: Median = 67 + 72/2 = 139/2 = 69.5 Hence, Option A is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 2023 Series IQuestion 2984 of 473

All Questions

The median of the observations $\displaystyle 42, 72, 35, 92, 67, 85, 72, 81, 51, 56$ is

Options

\displaystyle 69.5

\displaystyle 72

\displaystyle 64

\displaystyle 61.5

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Correct Answer

✅ Option a — $\displaystyle 69.5$

All Options:

A $\displaystyle 69.5$
B $\displaystyle 72$
C $\displaystyle 64$
D $\displaystyle 61.5$

Detailed Solution & Explanation

We are given the observations:

\displaystyle 42, 72, 35, 92, 67, 85, 72, 81, 51, 56

. 1. Arrange the data in ascending order:

35, 42, 51, 56, 67, 72, 72, 81, 85, 92

Here, the number of observations is

\displaystyle n = 10

. 2. The median is the average of the two middle-most observations (the

\displaystyle 5^{\text{th}}

and

\displaystyle 6^{\text{th}}

observations): -

\displaystyle 5^{\text{th}}

observation:

\displaystyle 67

\displaystyle 6^{\text{th}}

observation:

\displaystyle 72

3. Calculate the median:

\text{Median} = \frac{67 + 72}{2} = \frac{139}{2} = 69.5

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

Median

The middle value of a data set when arranged in ascending or descending order. It divides the distribution into two equal halves. For even n: Median = average of (n/2)th and (n/2 + 1)th values. It is NOT affected by extreme values.

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The median of the observations 42,72,35,92,67,85,72,81,51,56\displaystyle 42, 72, 35, 92, 67, 85, 72, 81, 51, 5642,72,35,92,67,85,72,81,51,56 is