For a given data set: 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4 , what is the median?

Option b: 6. Solution: We are given the data set: 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4 . 1. Arrange the data in ascending order: 2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19 Here, the number of observations is n = 15 (which is odd). 2. The median is the n+1/2th observation: Position of Median = 15 + 1/2 = 8th observation 3. The 8th observation in the sorted list is 6 . Therefore, the median of the dataset is 6 . Hence, Option B is the correct answer.

For a given data set: $5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4$, what is the median?

The correct answer is Option b: $6$. We are given the data set: $5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4$. 1. Arrange the data in ascending order: $$2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19$$ Here, the number of observations is $n = 15$ (which is odd). 2. The median is the $\frac{n+1}{2}^{\text{th}}$ observation: $$\text{Position of Median} = \frac{15 + 1}{2} = 8^{\text{th}} \text{ observation}$$ 3. The $8^{\text{th}}$ observation in the sorted list is $6$. Therefore, the median of the dataset is $6$. Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ Dec 23Question 2961 of 473

All Questions

For a given data set: $\displaystyle 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4$ , what is the median?

Options

\displaystyle 8

\displaystyle 6

\displaystyle 4

\displaystyle 9

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

Correct Answer

✅ Option b — $\displaystyle 6$

All Options:

A $\displaystyle 8$
B $\displaystyle 6$
C $\displaystyle 4$
D $\displaystyle 9$

Detailed Solution & Explanation

We are given the data set:

\displaystyle 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4

. 1. Arrange the data in ascending order:

2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19

Here, the number of observations is

\displaystyle n = 15

(which is odd). 2. The median is the

\displaystyle \frac{n+1}{2}^{\text{th}}

observation:

\text{Position of Median} = \frac{15 + 1}{2} = 8^{\text{th}} \text{ observation}

3. The

\displaystyle 8^{\text{th}}

observation in the sorted list is

\displaystyle 6

. Therefore, the median of the dataset is

\displaystyle 6

. 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

Set

A well-defined collection of distinct objects (called elements or members). Sets are denoted by capital letters and elements are listed within curly braces. Key operations include Union (∪), Intersection (∩), and Complement.

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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For a given data set: 5,10,3,6,4,8,9,3,15,2,9,4,19,11,4\displaystyle 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 45,10,3,6,4,8,9,3,15,2,9,4,19,11,4, what is the median?