The median of data 13, 8, 11, 6, 4, 15, 2, 18 is

Option d: 9.5. Solution: To find the median of the data: 13, 8, 11, 6, 4, 15, 2, 18 : 1. Arrange the data in ascending order: 2, 4, 6, 8, 11, 13, 15, 18 Here, the number of observations is n = 8 (which is even). 2. The median is the average of the two middle-most values (the 4th and 5th values): - 4th value: 8 - 5th value: 11 3. Calculate the median: Median = 8 + 11/2 = 19/2 = 9.5 Hence, Option D is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Apr 21Question 2976 of 473

All Questions

The median of data $\displaystyle 13, 8, 11, 6, 4, 15, 2, 18$ is

Options

\displaystyle 8

\displaystyle 9

\displaystyle 11

\displaystyle 9.5

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Correct Answer

✅ Option d — $\displaystyle 9.5$

All Options:

A $\displaystyle 8$
B $\displaystyle 9$
C $\displaystyle 11$
D $\displaystyle 9.5$

Detailed Solution & Explanation

To find the median of the data:

\displaystyle 13, 8, 11, 6, 4, 15, 2, 18

: 1. Arrange the data in ascending order:

2, 4, 6, 8, 11, 13, 15, 18

Here, the number of observations is

\displaystyle n = 8

(which is even). 2. The median is the average of the two middle-most values (the

\displaystyle 4^{\text{th}}

and

\displaystyle 5^{\text{th}}

values): -

\displaystyle 4^{\text{th}}

value:

\displaystyle 8

\displaystyle 5^{\text{th}}

value:

\displaystyle 11

3. Calculate the median:

\text{Median} = \frac{8 + 11}{2} = \frac{19}{2} = 9.5

Hence, **Option D** 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 data 13,8,11,6,4,15,2,18\displaystyle 13, 8, 11, 6, 4, 15, 2, 1813,8,11,6,4,15,2,18 is