If the relationship between x and y is 4x - 6y = 13 & median of x is 16 . Find median of y .

Option c: 8.50. Solution: We are given the relationship between x and y : 4x - 6y = 13 Since the median satisfies linear transformations, we can directly substitute the median value of x (which is 16 ) to find the median value of y : 4(Medianx) - 6(Mediany) = 13 4(16) - 6(Mediany) = 13 64 - 6(Mediany) = 13 6(Mediany) = 64 - 13 = 51 Mediany = 51/6 = 8.50 Hence, Option C is the correct answer.

If the relationship between $x$ and $y$ is $4x - 6y = 13$ & median of $x$ is $16$. Find median of $y$.

The correct answer is Option c: $8.50$. We are given the relationship between $x$ and $y$: $$4x - 6y = 13$$ Since the median satisfies linear transformations, we can directly substitute the median value of $x$ (which is $16$) to find the median value of $y$: $$4(\text{Median}_x) - 6(\text{Median}_y) = 13$$ $$4(16) - 6(\text{Median}_y) = 13$$ $$64 - 6(\text{Median}_y) = 13$$ $$6(\text{Median}_y) = 64 - 13 = 51$$ $$\text{Median}_y = \frac{51}{6} = 8.50$$ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IIQuestion 2987 of 473

All Questions

If the relationship between $\displaystyle x$ and $\displaystyle y$ is $\displaystyle 4x - 6y = 13$ & median of $\displaystyle x$ is $\displaystyle 16$ . Find median of $\displaystyle y$ .

Options

\displaystyle 7.50

\displaystyle 8

\displaystyle 8.50

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $\displaystyle 8.50$

All Options:

A $\displaystyle 7.50$
B $\displaystyle 8$
C $\displaystyle 8.50$
DNone of these

Detailed Solution & Explanation

We are given the relationship between

\displaystyle x

and

\displaystyle y

4x - 6y = 13

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

\displaystyle x

(which is

\displaystyle 16

) to find the median value of

\displaystyle y

4(\text{Median}_x) - 6(\text{Median}_y) = 13

4(16) - 6(\text{Median}_y) = 13

64 - 6(\text{Median}_y) = 13

6(\text{Median}_y) = 64 - 13 = 51

\text{Median}_y = \frac{51}{6} = 8.50

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.

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If the relationship between x\displaystyle xx and y\displaystyle yy is 4x−6y=13\displaystyle 4x - 6y = 134x−6y=13 & median of x\displaystyle xx is 16\displaystyle 1616. Find median of y\displaystyle yy.