Central Tendency & DispersionMTP Apr 21Question 3174 of 473
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Which measure of dispersion is based on all the observations?

Options

AMean Deviation
BStandard Deviation
CQuartile Deviation
DA and B but not C
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Correct Answer

✅ Option d — A and B but not C

All Options:

  • AMean Deviation
  • BStandard Deviation
  • CQuartile Deviation
  • DA and B but not C

Detailed Solution & Explanation

**Analysis of each measure:** - **Range:** Based only on 2 observations (max and min). - **Quartile Deviation (QD):** Based only on the middle 50% of observations (Q1\displaystyle Q_1 and Q3\displaystyle Q_3); extreme values are ignored. - **Mean Deviation (MD):** Calculated using all observations — MD=∑∣xi−xˉ∣n\displaystyle MD = \frac{\sum|x_i - \bar{x}|}{n}; uses all n\displaystyle n values. - **Standard Deviation (SD):** Calculated using all observations — σ=∑(xi−xˉ)2n\displaystyle \sigma = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n}}; uses all n\displaystyle n values. Both MD and SD use all observations. The best answer among the given options is **Option D: A and B but not C** (Mean Deviation AND Standard Deviation, but NOT Quartile Deviation). The given `correct_option` 'a' (Mean Deviation only) is incomplete since SD also uses all observations. Hence, **Option D** is the correct answer.

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