Question

Show your solution. 1. Given the following data: 11 18 24 33 47 59 61 72 Find each of the following. a. Q b. Q2 c. Pso d. Pes 2. IfS [0,1,2,3,4,5,6,7,8,9) and A [0,2,4,6,8), B [1,3,5,7,9), C - (23,4,5) and D-(1,6,7), List the elements of the sets corresponding to the following events: a. AUB b. AnB C.

Answer 1

Arrange the given data in ascending order

11 , 18 , 24 ,33 , 47 , 59 ,61 ,72

(I) Q₁ = [( n + 1)/4] th item

=[(8+1)/4] th item

= 2.25 th item

= 2nd item+ 0.25(3rd item - 2nd item)

= 18+(24-18)/4

= 19.5

(ii) Q₂ =[(n+1)/2] th item

=[(8+1)/2] th item

=4.5 th item

=4th item +(5th item - 4th item)/2

=33+(47-33)/2

=33+ 7

=40

P_{50= i(n+1)/100 th item}

_{=( 50× 9)/100 th item}

_{=4.5 th item}

_{=4th item+(5th item - 4th item)/2}

_{= 33+(47-33)/2}

_{= 40}

P₈₅= (85× 9)/100 th item

= 7.65 th item

= 7 th item +0.65(8th item - 7 th item)

=61+0.65(72-61)

= 68.15

2). S= { 0,1,2,3,4,5,6,7,8,9}

A={0,2,4,6,8}

B= {1,3,5,7,9}

C= {2,3,4,5}

D={1,6,7}

a) AUB={0,2,4,6,8}U{1,3,5,7,9}

={0,1,2,3,4,5,6,7,8,9}

b).A $\bigcap$​​​​​ B= { 0,2,4,6,8} $\bigcap$ { 1,3,5,7,9}

={ }

C) C' = S- C

={0,1,2,3,4,5,6,7,8,9}- { 2,3,4,5}

= {0,1,6,7,8,9}

d)D' =S-D

={0,2,3,4,5,8,9}

A$\bigcap$ C $\bigcap$ D'= {0,2,4,6,8} $\bigcap$ { 2,3,4,5} $\bigcap$ { 0,2,3,4,5,8,9}

={2,4,}