probablity and statistics Flashcards
mean of individual series
x = summation of X/N and x = a+ summation d/N
mean of discrete series
x = summation f/N and x = A + summation fd/N
mean on continuous series
x = summation f/N and x = A + summation fd/N
mode of individual series
most occurring number
mode of discrete series
max frequency
mode of continuous series
Mo = L + f1-f0 / 2f1-f0-f2 * h
median of individual series
1). N is odd: n+1/2 th term
2). N is even: average of n+/2th term and n+1/2th term
median of discrete series
arrange in ascending order
same as individual
median of continuous series
median class has cumulative frequency just above n/2
L + (N/2 - cf)/f * h (cf of preceeding class)
quartiles of individual series
Qm = m(N+1/4)th term
quartlies of discrete series
Qm = m(N+1/4)th term
quartiles of continuous series
L + (mN/4 - cf/f) * h
deciles of individual series
Dm = m(N+1/10)th term
deciles of continuous series
Dm = L + (mN/10 - cf/f) * h
percentiles of individual series
Pm = m(N+1/100)th term
percentiles of continuous series
Pm = L + (mN/100 - cf/f) * h
quartile deviation
Q3 - Q1/2
Mean deviation of individual series
M.D(x) = 1/n summation|xi - x|
M.D(M) = 1/n summation|xi - M|
Mean deviation of discrete & continuous series
M.D(x) = 1/N summation Fi|xi - x|
M.D(x) = 1/N summation Fi|xi - M|
Standard Deviation & Variance of individual series
sigma = sqrt of 1/N E(xi-x)^2
sigma^2 = 1/N E(xi-x)^2
Standard Deviation & Variance of Discrete series
sigma = sqrt of 1/N E fi(xi-x)^2
sigma^2 = 1/N E fi(xi-x)^2
Standard Deviation of continuous series (using xi)
sigma = 1/N sqrt of N E fixi^2 - (E fixi)^2
sigma^2 = 1/N^2 [ N E fixi^2 - (E fixi)^2]
Standard Deviation of continuous series (using ui)
sigma = h/N sqrt of N E fiui^2 - (E fivi)^2
sigma^2 = hsq/Nsq [ N E fivi^2 - (E fivi)^2
ui
xi-A/h
Relation between mean, mode, median
Mode = 3Median - 2Mean
Relation between QD, MD & SD
6QD = 5MD = 4 SD
Coefficient of variance
SD/mean * 100
sigma/x * 100
