Measures of Central Tendency and DispersionPYQ Jan 26Question 4585 of 473
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In continuous frequency distribution, the median of the data is 32. If each observation is increased by 7, then the new median will be:

Options

A39
B32
C25
D35
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Correct Answer

✅ Option a — 39

All Options:

  • A39
  • B32
  • C25
  • D35

Detailed Solution & Explanation

The median is a measure of central tendency. One of the key properties of the median is its behavior under linear transformations: If each observation xi\displaystyle x_i in a dataset is transformed to yi=xi+k\displaystyle y_i = x_i + k (where k\displaystyle k is a constant), then the new median of y\displaystyle y is: New Median=Original Median+k\text{New Median} = \text{Original Median} + k
We are given: - Original Median = 32\displaystyle 32 - Increase in each observation (k\displaystyle k) = 7\displaystyle 7
Substituting these values: New Median=32+7=39\text{New Median} = 32 + 7 = 39 Hence, **Option A** 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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