Measures of Central Tendency and DispersionMCQMTP Dec 22 - Series IQuestion 3189 of 473
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What is the SD of the following series : Meas. | 0-10 | 10-20 | 20-30 | 30-40 Freq. | 1 | 3 | 4 | 2

Options

A81
B7.6
C9
D2.26
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Correct Answer

✅ Option c — 9

All Options:

  • A81
  • B7.6
  • C9
  • D2.26

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Detailed Solution & Explanation

**Frequency Distribution:** ClassMid-point (m)Freq (f)0−105110−2015320−3025430−40352N=10\begin{array}{|c|c|c|} \hline \text{Class} & \text{Mid-point } (m) & \text{Freq } (f) \\ \hline 0-10 & 5 & 1 \\ 10-20 & 15 & 3 \\ 20-30 & 25 & 4 \\ 30-40 & 35 & 2 \\ \hline & & N = 10 \\ \hline \end{array} **Step 1: Calculate Mean.** xˉ=∑fm∑f=5(1)+15(3)+25(4)+35(2)10=5+45+100+7010=22010=22\bar{x} = \frac{\sum fm}{\sum f} = \frac{5(1)+15(3)+25(4)+35(2)}{10} = \frac{5+45+100+70}{10} = \frac{220}{10} = 22 **Step 2: Calculate ∑f(m−xˉ)2\displaystyle \sum f(m - \bar{x})^2.** mf(m−22)(m−22)2f(m−22)251−17289289153−749147254393635213169338∑=810\begin{array}{|c|c|c|c|c|} \hline m & f & (m-22) & (m-22)^2 & f(m-22)^2 \\ \hline 5 & 1 & -17 & 289 & 289 \\ 15 & 3 & -7 & 49 & 147 \\ 25 & 4 & 3 & 9 & 36 \\ 35 & 2 & 13 & 169 & 338 \\ \hline & & & & \sum = 810 \\ \hline \end{array} **Step 3: Calculate Variance.** σ2=∑f(m−xˉ)2N=81010=81\sigma^2 = \frac{\sum f(m-\bar{x})^2}{N} = \frac{810}{10} = 81 **Step 4: Calculate SD.** σ=81=9\sigma = \sqrt{81} = 9 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.

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