SET 1 QUESTION 1 (a) Class Boundaries Frequency, (f) Midpoint, (x) fx Cummulative Frequancy (F) 5 - 9 4.5 - 9.5 4 7 28 4 10 - 14 9.5 - 14.5 9 12 108 13 15 - 19 14.5 - 19.5 16 17 272 29 20 - 24 19.5 - 24.5 12 22 264 41 25 - 29 24.5 - 29.5 6 27 162 47 30 - 34 29.5 - 34.5 3 32 96 50 50 930 i. Mean f fx x Σ Σ = 18.6 50 930 x = = ii. Median, c f F N m l m m − = + 2 5 18.25 16 13 2 50 14.5 = − m = + (b) i. N x x Σ = 5 2 5 3 3 4 2 7 7 − + + + + + − + + = x x x x x 7 5 8 9 = x + 3.25 8 9 35 = + = x x
ii. (x − 2),(x + 5),(x + 3),(3x − 4),(2x + 7) = 1.25, 8.25, 6.25, 5.75, 13.5 Median =1.25, 5.75, 6.25, 8.25, 13.5 3 2 5 1 2 1 = + = + = N = 6.25 Mode = no mode (c) ii. A box contains of 20 red marbles, 32 blue marbles, 17 yellow marbles and 11 white marbles. A marble is picked randomly from the box. Calculate the probability of picking a red marble. 0.25 4 1 80 20 ( ) ( ) ( ) = = = = n S n A P A iii. Ten pieces of paper numbered from 21 to 30 are placed in a file. A piece of paper is picked at random from the file. Calculate the probability of picking a number that is even OR divisible by 3. Non –Mutually exclusive event {S}= {21,22,23,24,25,26,27,28,29,30}, n(s) = 10 { } { } { } { } {21,24,27,30}, { } 4 22,24,26,28,30 , 5 = = = = P D n D P E n E (E ∪ D) = {21,22,24,26,27,28,30}, n(E ∪ D) = 7 (E ∩ D) = {24,30},n(E ∩ D) = 2 Method 1 10 7 ( ) ( ) ( ) = ∪ ∪ = n S n E D P E D OR Method 2 10 7 10 2 10 4 10 5 ( ) ( ) ( ) ( ) ( ) ∪ = + − = ∪ = + − ∩ P E D P E D P E P D P E D