Central Tendency & DispersionPYQ Nov. 19Question 3125 of 473
All Questions

Find SD of the following 1,2,3,4,5,6,7,8,9.\displaystyle 1, 2, 3, 4, 5, 6, 7, 8, 9.

Options

A2.56\displaystyle 2.56
B60/9\displaystyle 60/9
C60/3\displaystyle 60/3
D3.20\displaystyle 3.20
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — 2.56\displaystyle 2.56

All Options:

  • A2.56\displaystyle 2.56
  • B60/9\displaystyle 60/9
  • C60/3\displaystyle 60/3
  • D3.20\displaystyle 3.20

Detailed Solution & Explanation

We want to find the standard deviation (S.D.) of the first 9\displaystyle 9 natural numbers (1,2,…,9\displaystyle 1, 2, \dots, 9). The standard deviation of the first n\displaystyle n natural numbers is given by the formula: S.D.=n2−112\text{S.D.} = \sqrt{\frac{n^2 - 1}{12}} Substituting n=9\displaystyle n = 9: S.D.=92−112=81−112=8012=203≈6.67≈2.58\text{S.D.} = \sqrt{\frac{9^2 - 1}{12}} = \sqrt{\frac{81 - 1}{12}} = \sqrt{\frac{80}{12}} = \sqrt{\frac{20}{3}} \approx \sqrt{6.67} \approx 2.58 Hence, **Option A** 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