The first Quartile is 142 and Semi-inter Quartile Range is 18 , then the value of Median is:

Option b: 160. Solution: We are given: - First quartile: Q1 = 142 - Semi-interquartile range (Quartile Deviation, Q.D.): Q.D. = 18 For a symmetric distribution, the quartiles are symmetric about the median, which means: Q.D. = Q3 - Q1/2 Q3 - Q1 = 2(18) = 36 Q3 = 142 + 36 = 178 Also, the median is the midpoint of Q1 and Q3 : Median = Q1 + Q3/2 = 142 + 178/2 = 320/2 = 160 Alternatively, we can directly compute: Median = Q1 + Q.D. = 142 + 18 = 160 Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 22/ MTP Sep 24 IQuestion 2980 of 473

All Questions

The first Quartile is $\displaystyle 142$ and Semi-inter Quartile Range is $\displaystyle 18$ , then the value of Median is:

Options

\displaystyle 151

\displaystyle 160

\displaystyle 178

DNone of these

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Correct Answer

✅ Option b — $\displaystyle 160$

All Options:

A $\displaystyle 151$
B $\displaystyle 160$
C $\displaystyle 178$
DNone of these

Detailed Solution & Explanation

We are given: - First quartile:

\displaystyle Q_1 = 142

- Semi-interquartile range (Quartile Deviation, Q.D.):

\displaystyle \text{Q.D.} = 18

For a symmetric distribution, the quartiles are symmetric about the median, which means:

\text{Q.D.} = \frac{Q_3 - Q_1}{2} \implies Q_3 - Q_1 = 2(18) = 36 \implies Q_3 = 142 + 36 = 178

Also, the median is the midpoint of

\displaystyle Q_1

and

\displaystyle Q_3

\text{Median} = \frac{Q_1 + Q_3}{2} = \frac{142 + 178}{2} = \frac{320}{2} = 160

Alternatively, we can directly compute:

\text{Median} = Q_1 + \text{Q.D.} = 142 + 18 = 160

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.

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 first Quartile is 142\displaystyle 142142 and Semi-inter Quartile Range is 18\displaystyle 1818, then the value of Median is: