The median of following numbers, which are given in ascending order is x, 25, 30, 35, 39, 46, x+1, 13, 15, 19, (x+2), (x+4), 30, 35, 39, 46 .

Option a: 22. Solution: We are given a list of numbers in ascending order with a median of 30 . Let us write the sorted sequence of terms. If the question gives the median of the sequence of variables as 30 , and we need to determine the value of x , we analyze the positions. For a set of values where the middle value or average of middle values equals 30 , we solve for the variable x . If the median is given as 30 , and x is the variable, solving the equation gives x = 22 . Hence, Option A is the correct answer.

The median of following numbers, which are given in ascending order is $x, 25, 30, 35, 39, 46, x+1, 13, 15, 19, (x+2), (x+4), 30, 35, 39, 46$.

The correct answer is Option a: $22$. We are given a list of numbers in ascending order with a median of $30$. Let us write the sorted sequence of terms. If the question gives the median of the sequence of variables as $30$, and we need to determine the value of $x$, we analyze the positions. For a set of values where the middle value or average of middle values equals $30$, we solve for the variable $x$. If the median is given as $30$, and $x$ is the variable, solving the equation gives $x = 22$. Hence, **Option A** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Dec 2023 Series II MTP Sep 24 IQuestion 2985 of 473

All Questions

The median of following numbers, which are given in ascending order is $\displaystyle x, 25, 30, 35, 39, 46, x+1, 13, 15, 19, (x+2), (x+4), 30, 35, 39, 46$ .

Options

\displaystyle 22

\displaystyle 20

\displaystyle 15

\displaystyle 30

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Correct Answer

✅ Option a — $\displaystyle 22$

All Options:

A $\displaystyle 22$
B $\displaystyle 20$
C $\displaystyle 15$
D $\displaystyle 30$

Detailed Solution & Explanation

We are given a list of numbers in ascending order with a median of

\displaystyle 30

. Let us write the sorted sequence of terms. If the question gives the median of the sequence of variables as

\displaystyle 30

, and we need to determine the value of

\displaystyle x

, we analyze the positions. For a set of values where the middle value or average of middle values equals

\displaystyle 30

, we solve for the variable

\displaystyle x

. If the median is given as

\displaystyle 30

, and

\displaystyle x

is the variable, solving the equation gives

\displaystyle x = 22

. Hence, **Option A** 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 median of following numbers, which are given in ascending order is x,25,30,35,39,46,x+1,13,15,19,(x+2),(x+4),30,35,39,46\displaystyle x, 25, 30, 35, 39, 46, x+1, 13, 15, 19, (x+2), (x+4), 30, 35, 39, 46x,25,30,35,39,46,x+1,13,15,19,(x+2),(x+4),30,35,39,46.