Central Tendency & DispersionMTP 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

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.

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