Statistics

Question 1

Arithmetic mean for raw data

Answer 1

x̄ = Σ xᵢ / n

Question 2

A.M of an A.P

Answer 2

(first term + last term) / 2

Question 3

When is mean deviation minimum?

Answer 3

Mean deviation is minimum when deviations are taken from median

Question 4

Variance

Answer 4

σ= (Σxᵢ² )/n - x̄²

Question 5

Standard deviation

Answer 5

• √variance
• √[ (Σxᵢ² )/n - x̄ ]

Question 6

Coefficient of variance (C.V)

Answer 6

C.V = (S.D/ A.M)× 100

Question 7

Sum of first n natural numbers

Answer 7

n(n+1)/2

Question 8

Sum of square of first n natural numbers

Answer 8

n(n+1)(2n+1) / 6

Question 9

What is mode?

Answer 9

The value that appears the most frequently

Question 10

What is median?

Answer 10

Middle value in a sorted list

Question 11

If the standard deviation of x1, x2, x3…xn = σ. Then the standard deviation of ax1 + b, ax2 + b, ax3 + b…. = ?

Answer 11

aσ

Question 12

Relationship between mode, median and mean

Answer 12

Mode = 3 median - 2 mean

Question 13

AM ( x ± a) =

Answer 13

AM(x) ± a

Question 14

AM(ax)

Answer 14

a AM(x)

Question 15

Variance (x ± a) =

Answer 15

Variance (x)

Question 16

Variance (ax) =

Answer 16

a² variance (x)

Question 17

AM (ax + b) =

Answer 17

a AM(x) + b

Question 18

Combined mean

Answer 18

x̄= (n₁x̄₁ + n₂x̄₂) ÷ ( n₁ + n₂)

Question 19

Variance of first n natural numbers

Answer 19

(n² - 1)/12

Question 20

Variance of first n even natural numbers
OR
Variance of first n odd natural numbers

Answer 20

(n² - 1) /3