Onlinetuition.com SPM Mathematics
Question 7:Diagram below shows 4 cards labelled with letters.Two cards are chosen at random from the box, one by one, without replacement.(a) List the sample space.(b) Find the probability that(i) at least one card chosen is labelled C,(ii) both cards chosen are labelled with same letter.Solution:(a)Sample space, S= {(C, O1), (C, O2), (C, L), (O1, … Read more
Question 5:A fair dice is tossed. Then a card is picked at random from a box containing a yellow, a red and a purple card.(a) By using the letter Y to represent the yellow card, the letter R to represent the red card and the letter P to represent the purple card, complete the sample … Read more
Question 5:In an office, 300 workers go to work by bus, 60 workers go by car and the rest go by motorcycle. A worker is chosen at random. The probability of choosing a worker who goes to work by bus is ⅔.Find the probability of choosing a worker who does not go to work by … Read more
Question 9: The mean of the data 1, a, 2a, 8, 9 and 15 which has been arranged in ascending order is b. If each number of the data is subtracted by 3, the new median is 4 7 b . Find (a) The values of a and b, (b) The variance of the new … Read more
Question 7: A set of data consists of twelve positive numbers. It is given that Σ ( x− x ¯ ) 2 =600 and Σ x 2 =1032. Find (a) the variance (b) the mean Solution: (a) Variance= Σ ( x− x ¯ ) 2 N = 600 12 =50 (b) Variance= Σ x 2 N − ( x ¯ ) … Read more
Question 5: A set of data consists of 9, 2, 7, x2 – 1 and 4. Given the mean is 6, find (a) the positive value of x, (b) the median using the value of x in part (a). Solution: (a) Mean=6 9+2+7+ x 2 −1+4 5 =6 x 2 +21=30 x 2 … Read more
Question 3: The mean of five numbers is p . The sum of the squares of the numbers is 120 and the standard deviation is 2q. Express p in terms of q. Solution: Mean x ¯ = ∑ x N p = ∑ x 5 ∑ x = 5 p Standard deviation, σ = ∑ x … Read more
Question 1: Given that the standard deviation of five numbers is 6 and the sum of the squares of these five numbers is 260. Find the mean of this set of numbers. Solution: Given that σ = 6 , Σ x 2 = 260. σ = 6 Σ x 2 n − X ¯ 2 = … Read more
Variance and Standard Deviation 1. The variance is a measure of the mean for the square of the deviations from the mean. 2. The standard deviation refers to the square root for the variance. (A) Ungrouped Data Example 1: Find the variance and standard deviation of the following data. 15, 17, 21, 24 and 31 Solution: Variance, σ … Read more
(A) Interquartile Range of Ungrouped Data Example 1: Find the interquartile range of the following data. (a) 7, 5, 1, 3, 6, 11, 8 (b) 12, 4, 6, 18, 9, 16, 2, 14 Solution: (a) Rearrange the data according to ascending order. Interquartile Range = upper quartile – lower quartile = 8 – 3 = 5 … Read more