The relationship between two variables x and y is given by 4x - 10y = 20 . If the median value of the variable x is 10 then what is median value of variable y ?

Option b: 2.0. Solution: We are given the relationship between the two variables x and y : 4x - 10y = 20 Since partition values (like the median) satisfy the linear relationship directly, we can substitute the median value of x (which is 10 ) into the equation to find the median value of y : 4(Medianx) - 10(Mediany) = 20 4(10) - 10(Mediany) = 20 40 - 10(Mediany) = 20 10(Mediany) = 20 Mediany = 2.0 Hence, Option B is the correct answer.

The relationship between two variables $x$ and $y$ is given by $4x - 10y = 20$. If the median value of the variable $x$ is 10 then what is median value of variable $y$?

The correct answer is Option b: 2.0. We are given the relationship between the two variables $x$ and $y$: $$4x - 10y = 20$$ Since partition values (like the median) satisfy the linear relationship directly, we can substitute the median value of $x$ (which is $10$) into the equation to find the median value of $y$: $$4(\text{Median}_x) - 10(\text{Median}_y) = 20$$ $$4(10) - 10(\text{Median}_y) = 20$$ $$40 - 10(\text{Median}_y) = 20$$ $$10(\text{Median}_y) = 20 \implies \text{Median}_y = 2.0$$ Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Dec 22Question 2948 of 473

All Questions

The relationship between two variables $\displaystyle x$ and $\displaystyle y$ is given by $\displaystyle 4x - 10y = 20$ . If the median value of the variable $\displaystyle x$ is 10 then what is median value of variable $\displaystyle y$ ?

Options

A4.0

B2.0

C3.0

D4.0

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

Correct Answer

✅ Option b — 2.0

All Options:

A4.0
B2.0
C3.0
D4.0

Detailed Solution & Explanation

We are given the relationship between the two variables

\displaystyle x

and

\displaystyle y

4x - 10y = 20

Since partition values (like the median) satisfy the linear relationship directly, we can substitute the median value of

\displaystyle x

(which is

\displaystyle 10

) into the equation to find the median value of

\displaystyle y

4(\text{Median}_x) - 10(\text{Median}_y) = 20

4(10) - 10(\text{Median}_y) = 20

40 - 10(\text{Median}_y) = 20

10(\text{Median}_y) = 20 \implies \text{Median}_y = 2.0

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 relationship between two variables x\displaystyle xx and y\displaystyle yy is given by 4x−10y=20\displaystyle 4x - 10y = 204x−10y=20. If the median value of the variable x\displaystyle xx is 10 then what is median value of variable y\displaystyle yy?