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)
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