Central Tendency & DispersionMTP June 22Question 3184 of 473
All Questions

SD of first five consecutive natural numbers is:

Options

A10\displaystyle \sqrt{10}
B8\displaystyle \sqrt{8}
C3\displaystyle \sqrt{3}
D2\displaystyle \sqrt{2}
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — 2\displaystyle \sqrt{2}

All Options:

  • A10\displaystyle \sqrt{10}
  • B8\displaystyle \sqrt{8}
  • C3\displaystyle \sqrt{3}
  • D2\displaystyle \sqrt{2}

Detailed Solution & Explanation

**Given:** First 5 natural numbers: 1, 2, 3, 4, 5. n=5\displaystyle n = 5 **Method 1: Direct computation** xˉ=1+2+3+4+55=3\bar{x} = \frac{1+2+3+4+5}{5} = 3 ∑(xi−xˉ)2=(1−3)2+(2−3)2+(3−3)2+(4−3)2+(5−3)2\sum(x_i - \bar{x})^2 = (1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2 =4+1+0+1+4=10= 4+1+0+1+4 = 10 σ2=105=2\sigma^2 = \frac{10}{5} = 2 σ=2\sigma = \sqrt{2} **Method 2: Formula** σ=n2−112=25−112=2412=2\sigma = \sqrt{\frac{n^2-1}{12}} = \sqrt{\frac{25-1}{12}} = \sqrt{\frac{24}{12}} = \sqrt{2} Hence, **Option D** is the correct answer.

More Questions from Central Tendency & Dispersion

If the range of 28,22,40,20,15,50\displaystyle 28, 22, 40, 20, 15, 50 is

If the S.D. of the 1st\displaystyle 1^{st} n\displaystyle n natural numbers is 30\displaystyle \sqrt{30} then the value of n\displaystyle n is

If the variance of 5,7,9\displaystyle 5, 7, 9 and 11\displaystyle 11 is 4\displaystyle 4, then the coefficient of variation is:

A helicopter flies from A to B at the rate of 500 km/hr. and comes back at the rate 700 km/hr. The average speed of the helicopter is

If Arithmetic Mean (A.M.) and Geometric Mean (G.M.) of two numbers are 6.50 and 6 respectively, then the two numbers are

Which of the following is not a method of dispersion?

Ready to Master Central Tendency & Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free