The wages of 8 workers expressed in rupees are 42,45,49,38,56,54,55,47 . Find median wage?

Option b: 48. Solution: We are given the wages of 8 workers: 42, 45, 49, 38, 56, 54, 55, 47 : 1. Arrange the wages in ascending order: 38, 42, 45, 47, 49, 54, 55, 56 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 terms): - 4th term: 47 - 5th term: 49 3. Calculate the median wage: Median = 47 + 49/2 = 96/2 = 48 Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IIQuestion 2989 of 473

All Questions

The wages of $\displaystyle 8$ workers expressed in rupees are $\displaystyle 42,45,49,38,56,54,55,47$ . Find median wage?

Options

\displaystyle 47

\displaystyle 48

\displaystyle 49

\displaystyle 50

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Correct Answer

✅ Option b — $\displaystyle 48$

All Options:

A $\displaystyle 47$
B $\displaystyle 48$
C $\displaystyle 49$
D $\displaystyle 50$

Detailed Solution & Explanation

We are given the wages of 8 workers:

\displaystyle 42, 45, 49, 38, 56, 54, 55, 47

: 1. Arrange the wages in ascending order:

38, 42, 45, 47, 49, 54, 55, 56

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}}

terms): -

\displaystyle 4^{\text{th}}

term:

\displaystyle 47

\displaystyle 5^{\text{th}}

term:

\displaystyle 49

3. Calculate the median wage:

\text{Median} = \frac{47 + 49}{2} = \frac{96}{2} = 48

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 wages of 8\displaystyle 88 workers expressed in rupees are 42,45,49,38,56,54,55,47\displaystyle 42,45,49,38,56,54,55,4742,45,49,38,56,54,55,47. Find median wage?