Central Tendency & DispersionMTP May 19Question 2970 of 473
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What is the value of the first quartile for observations 15,18,10,20,23,28,12,16\displaystyle 15, 18, 10, 20, 23, 28, 12, 16?

Options

A17\displaystyle 17
B16\displaystyle 16
C12.75\displaystyle 12.75
D12\displaystyle 12
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Correct Answer

✅ Option c — 12.75\displaystyle 12.75

All Options:

  • A17\displaystyle 17
  • B16\displaystyle 16
  • C12.75\displaystyle 12.75
  • D12\displaystyle 12

Detailed Solution & Explanation

To find the first quartile (Q1\displaystyle Q_1) for the observations: 15,18,10,20,23,28,12,16\displaystyle 15, 18, 10, 20, 23, 28, 12, 16: 1. Arrange the data in ascending order: 10,12,15,16,18,20,23,2810, 12, 15, 16, 18, 20, 23, 28 Here, the number of observations is n=8\displaystyle n = 8. 2. The position of Q1\displaystyle Q_1 is given by: Position of Q1=n+14=8+14=2.25th observation\text{Position of } Q_1 = \frac{n+1}{4} = \frac{8+1}{4} = 2.25^{\text{th}} \text{ observation} 3. Calculate the value of the 2.25th\displaystyle 2.25^{\text{th}} observation: Q1=2nd observation+0.25×(3rd observation−2nd observation)Q_1 = 2^{\text{nd}} \text{ observation} + 0.25 \times (3^{\text{rd}} \text{ observation} - 2^{\text{nd}} \text{ observation}) Q1=12+0.25×(15−12)=12+0.25×3=12.75Q_1 = 12 + 0.25 \times (15 - 12) = 12 + 0.25 \times 3 = 12.75 Hence, **Option C** is the correct answer.

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