Points to Remember
· Range = L–S (L - Largest value, S - Smallest value)
· Coefficient of range = ; Variance
· Standard deviation
· Standard deviation (ungrouped data)
· Standard deviation of first n natural numbers
· Standard deviation (grouped data)
· Coefficient of variation C.V = × 100%
· If the C.V. value is less, then the observations of corresponding data are consistent.
If the C.V. value is more then the observations of corresponding are inconsistent.
· In a random experiment, the set of all outcomes are known but exact outcome is not known.
· The set of all possible outcomes is called sample space.
· A, B are said to be mutually exclusive events if A ∩ B = ɸ
· Probability of event E is P (E) = n(E)/n(S)
(i) The probability of sure event is 1 and the probability of impossible event is 0.
(ii) 0 ≤ P (E) ≤ 1 ;(iii) P () = 1 − P (E)
· If A and B are mutually exclusive events then P (A ∪ B ) = P(A) + P(B) .
(i) P (A ∩ ) = P (onlyA) = P (A) – P (A ∩ B)
(ii) P (A ∩ ) = P (onlyB) = P (B) – P (A ∩ B)
· P (A U B) = P (A) + P (B) – P (A ∩ B) , for any two events A, B.
· For any three events A, B, C
P (A U B UC) = P (A) + P (B) + P (C) − P (A ∩ B ) − P(B ∩C) −P (C ∩ A) + P(A ∩ B ∩C)