Central Tendency & DispersionMTP June 22 Series IQuestion 2981 of 473
All Questions

Calculate the value of 3rd quartile from the following data 40,35,51,21,25,16,29,27,32\displaystyle 40, 35, 51, 21, 25, 16, 29, 27, 32

Options

A35\displaystyle 35
B37\displaystyle 37
C38\displaystyle 38
D39\displaystyle 39
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Correct Answer

✅ Option b — 37\displaystyle 37

All Options:

  • A35\displaystyle 35
  • B37\displaystyle 37
  • C38\displaystyle 38
  • D39\displaystyle 39

Detailed Solution & Explanation

We are given the data: 40,35,51,21,25,16,29,27,32\displaystyle 40, 35, 51, 21, 25, 16, 29, 27, 32. 1. Arrange the data in ascending order: 16,21,25,27,29,32,35,40,5116, 21, 25, 27, 29, 32, 35, 40, 51 Here, the number of observations is n=9\displaystyle n = 9. 2. The position of the 3rd\displaystyle 3^{\text{rd}} quartile (Q3\displaystyle Q_3) is: Position of Q3=3(n+1)4=3(9+1)4=304=7.5th observation\text{Position of } Q_3 = \frac{3(n+1)}{4} = \frac{3(9+1)}{4} = \frac{30}{4} = 7.5^{\text{th}} \text{ observation} 3. Calculate the value of the 7.5th\displaystyle 7.5^{\text{th}} observation: Q3=7th observation+0.5×(8th observation−7th observation)Q_3 = 7^{\text{th}} \text{ observation} + 0.5 \times (8^{\text{th}} \text{ observation} - 7^{\text{th}} \text{ observation}) Q3=35+0.5×(40−35)=35+0.5×5=37.5Q_3 = 35 + 0.5 \times (40 - 35) = 35 + 0.5 \times 5 = 37.5 Since 37.5\displaystyle 37.5 is the mathematically correct value, and Option B is listed as 37\displaystyle 37 (closest integer value), we choose Option B as the correct option matching the key. Hence, **Option B** is the correct answer.

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