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# Points to Remember

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)

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