The mode of data is 18 and mean is 24 , then median is

Option c: 22. Solution: Step 1: Apply the empirical formula. Mode = 3Median - 2Mean Step 2: Substitute values. - Mode = 18, Mean = 24 18 = 3Median - 48 3Median = 66 Median = 22 Hence, Option C is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 23 Series IIQuestion 3065 of 473

All Questions

The mode of data is $\displaystyle 18$ and mean is $\displaystyle 24$ , then median is

Options

\displaystyle 18

\displaystyle 24

\displaystyle 22

\displaystyle 21

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Correct Answer

✅ Option c — $\displaystyle 22$

All Options:

A $\displaystyle 18$
B $\displaystyle 24$
C $\displaystyle 22$
D $\displaystyle 21$

Detailed Solution & Explanation

**Step 1: Apply the empirical formula.**

\text{Mode} = 3\text{Median} - 2\text{Mean}

**Step 2: Substitute values.** - Mode = 18, Mean = 24

18 = 3\text{Median} - 48

3\text{Median} = 66

\text{Median} = 22

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.

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.

Mode

The value that appears most frequently in a data set. A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes). It is the only measure of central tendency applicable to qualitative (categorical) data.

Related Comparison Tables

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The mode of data is 18\displaystyle 1818 and mean is 24\displaystyle 2424, then median is