probablity and statistics

Question 1

mean of individual series

Answer 1

x = summation of X/N and x = a+ summation d/N

Question 2

mean of discrete series

Answer 2

x = summation f/N and x = A + summation fd/N

Question 3

mean on continuous series

Answer 3

x = summation f/N and x = A + summation fd/N

Question 4

mode of individual series

Answer 4

most occurring number

Question 5

mode of discrete series

Answer 5

max frequency

Question 6

mode of continuous series

Answer 6

Mo = L + f1-f0 / 2f1-f0-f2 * h

Question 7

median of individual series

Answer 7

1). N is odd: n+1/2 th term
2). N is even: average of n+/2th term and n+1/2th term

Question 8

median of discrete series

Answer 8

arrange in ascending order
same as individual

Question 9

median of continuous series

Answer 9

median class has cumulative frequency just above n/2

L + (N/2 - cf)/f * h (cf of preceeding class)

Question 10

quartiles of individual series

Answer 10

Qm = m(N+1/4)th term

Question 11

quartlies of discrete series

Answer 11

Qm = m(N+1/4)th term

Question 12

quartiles of continuous series

Answer 12

L + (mN/4 - cf/f) * h

Question 13

deciles of individual series

Answer 13

Dm = m(N+1/10)th term

Question 14

deciles of continuous series

Answer 14

Dm = L + (mN/10 - cf/f) * h

Question 15

percentiles of individual series

Answer 15

Pm = m(N+1/100)th term

Question 16

percentiles of continuous series

Answer 16

Pm = L + (mN/100 - cf/f) * h

Question 17

quartile deviation

Answer 17

Q3 - Q1/2

Question 18

Mean deviation of individual series

Answer 18

M.D(x) = 1/n summation|xi - x|
M.D(M) = 1/n summation|xi - M|

Question 19

Mean deviation of discrete & continuous series

Answer 19

M.D(x) = 1/N summation Fi|xi - x|
M.D(x) = 1/N summation Fi|xi - M|

Question 20

Standard Deviation & Variance of individual series

Answer 20

sigma = sqrt of 1/N E(xi-x)^2
sigma^2 = 1/N E(xi-x)^2

Question 21

Standard Deviation & Variance of Discrete series

Answer 21

sigma = sqrt of 1/N E fi(xi-x)^2
sigma^2 = 1/N E fi(xi-x)^2

Question 22

Standard Deviation of continuous series (using xi)

Answer 22

sigma = 1/N sqrt of N E fixi^2 - (E fixi)^2
sigma^2 = 1/N^2 [ N E fixi^2 - (E fixi)^2]

Question 23

Standard Deviation of continuous series (using ui)

Answer 23

sigma = h/N sqrt of N E fiui^2 - (E fivi)^2
sigma^2 = hsq/Nsq [ N E fivi^2 - (E fivi)^2

Question 24

ui

Answer 24

xi-A/h

Question 25

Relation between mean, mode, median

Answer 25

Mode = 3Median - 2Mean

Question 26

Relation between QD, MD & SD

Answer 26

6QD = 5MD = 4 SD

Question 27

Coefficient of variance

Answer 27

SD/mean * 100

sigma/x * 100