Mathematics : Statistics And Probability: Points to Remember

**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)*

Tags : Statistics and Probability | Mathematics Statistics and Probability | Mathematics

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