Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2013MathematicsStatisticsActual

What is the variance of the first 11 natural numbers?

Options

  1. A10
  2. B11
  3. C12
  4. D13

Correct answer

A. 10

Step-by-step solution

Variance : The square of standard deviation is called the variance ( ^2 ) ^2= (x- X )^2 n , where X = mean of given data x = mean of 1st eleven natural numbers. = 11 12 2 11 =6 ^2= (1-6)^2+(2-6)^2+(3-6)^2+ +(11-6)^2 11 = 2 [1^2+2^2+3^2+4^2+5^2 ] 11 = 2 5 6 11 11 6 =10 .

Practice Statistics on Quantrex Academy →

More from Statistics

Let two lines of regression be x+y+11=0 and 2x+3y+4=0 for some data. What is the value of correlation coefficient between x and y ? 2026Passage: The frequency distribution of marks obtained by 100 students in a certain subject is given below : Marks 0 - 10 10 - 20 20 - 30 30 - 40 No. of students 10 20 f 40 Question 2026The standard deviation of 100 observations is 10 . If 5 is multiplied to each of the observations, then what is the new standard deviation ? 2026Passage: The frequency distribution of marks obtained by 100 students in a certain subject is given below : Marks 0 - 10 10 - 20 20 - 30 30 - 40 No. of students 10 20 f 40 Question 2026If the mean of 20 observations, namely x₁,x₂,x₃, ,x₂₀ is 1 414 , then what is the value of _ i=1 ²⁰100(2x_i+4) ? 2026If the random variable X has mean 3 and standard deviation 5 , then what is the variance of the random variable Y=2X-5 ? 2026The standard deviation of 100 observations is 10. If 20 is added to each observation, then what will be the new standard deviation? 2025Consider the following statements: I. Mean and variance have the same unit of measurement. II. Mean deviation and standard deviation have the same unit of measurement. Which of the 2025 Full Statistics list All NDA PYQs