Measures of Central Tendency and DispersionMCQMTP Nov 19Question 2972 of 473

Two variables $\displaystyle x$ and $\displaystyle y$ are given by $\displaystyle y = 2x - 3$ . If the median of $\displaystyle x$ is $\displaystyle 20$ , what is the median of $\displaystyle y$ ?

Options

\displaystyle 20

\displaystyle 35

\displaystyle 37

\displaystyle 40

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Correct Answer

✅ Option c — $\displaystyle 37$

All Options:

A $\displaystyle 20$
B $\displaystyle 35$
C $\displaystyle 37$
D $\displaystyle 40$

Detailed Solution & Explanation

We are given the relationship between two variables

\displaystyle x

and

\displaystyle y

y = 2x - 3

Since the median satisfies linear transformations, we can directly substitute the median value of

\displaystyle x

(which is

\displaystyle 20

) to find the median value of

\displaystyle y

\text{Median}_y = 2(\text{Median}_x) - 3

\text{Median}_y = 2(20) - 3 = 40 - 3 = 37

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.

Related Comparison Tables

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Two variables x\displaystyle xx and y\displaystyle yy are given by y=2x−3\displaystyle y = 2x - 3y=2x−3. If the median of x\displaystyle xx is 20\displaystyle 2020, what is the median of y\displaystyle yy?