Measures of Central Tendency and DispersionMCQPYQ June 22Question 2946 of 473
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Along a road there are 5 buildings of apartments, marked as 1,2,3,4,5\displaystyle 1, 2, 3, 4, 5. Number of people residing in each building is available. A bus stop is to be setup near one of the buildings so that the total distance walked by the resident to the bus stop from their buildings must be kept minimum. One must consider investing ________ to find the position of the bus stop.

Options

AMean
BMedian
CMode
DWeighted mean
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Correct Answer

✅ Option b — Median

All Options:

  • AMean
  • BMedian
  • CMode
  • DWeighted mean

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Detailed Solution & Explanation

To find the location of a service point (like a bus stop) along a line such that the sum of absolute distances walked by all residents is minimized, we apply a fundamental mathematical principle: the sum of the absolute deviations of a set of observations is minimized when the deviations are taken from the **Median**. Specifically, if x1,x2,…,xn\displaystyle x_1, x_2, \dots, x_n are the positions of the buildings, we want to choose a\displaystyle a to minimize ∑∣xi−a∣\displaystyle \sum |x_i - a|. This minimum is achieved when a\displaystyle a is the Median of the distribution. Therefore, the Median must be considered. 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.

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