The median value of the set of observations 48, 36, 72, 87, 19, 66, 56 and 91

Option c: 61. Solution: We are given the set of observations: 48, 36, 72, 87, 19, 66, 56, 91 . 1. Arrange the observations in ascending order: 19, 36, 48, 56, 66, 72, 87, 91 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: 56 - 5th value: 66 3. Calculate the median: Median = 56 + 66/2 = 122/2 = 61 Hence, Option C is the correct answer.

The median value of the set of observations $48, 36, 72, 87, 19, 66, 56$ and $91$

The correct answer is Option c: $61$. We are given the set of observations: $48, 36, 72, 87, 19, 66, 56, 91$. 1. Arrange the observations in ascending order: $$19, 36, 48, 56, 66, 72, 87, 91$$ Here, the number of observations is $n = 8$ (which is even). 2. The median is the average of the two middle-most values (the $4^{\text{th}}$ and $5^{\text{th}}$ values): - $4^{\text{th}}$ value: $56$ - $5^{\text{th}}$ value: $66$ 3. Calculate the median: $$\text{Median} = \frac{56 + 66}{2} = \frac{122}{2} = 61$$ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP March 22Question 2979 of 473

All Questions

The median value of the set of observations $\displaystyle 48, 36, 72, 87, 19, 66, 56$ and $\displaystyle 91$

Options

\displaystyle 53

\displaystyle 87

\displaystyle 61

\displaystyle 19

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Correct Answer

✅ Option c — $\displaystyle 61$

All Options:

A $\displaystyle 53$
B $\displaystyle 87$
C $\displaystyle 61$
D $\displaystyle 19$

Detailed Solution & Explanation

We are given the set of observations:

\displaystyle 48, 36, 72, 87, 19, 66, 56, 91

. 1. Arrange the observations in ascending order:

19, 36, 48, 56, 66, 72, 87, 91

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 56

\displaystyle 5^{\text{th}}

value:

\displaystyle 66

3. Calculate the median:

\text{Median} = \frac{56 + 66}{2} = \frac{122}{2} = 61

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

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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The median value of the set of observations 48,36,72,87,19,66,56\displaystyle 48, 36, 72, 87, 19, 66, 5648,36,72,87,19,66,56 and 91\displaystyle 9191