Key Concepts: Statistics involves collecting, analyzing, and interpreting data. Measures of central tendency include mean, median, and mode. Measures of spread include range and standard deviation. Probability is the likelihood of an event occurring, ranging from 0 to 1.
Section A: Data Analysis and Averages
1. The test scores of 10 students are: 45, 52, 61, 58, 71, 48, 65, 59, 74, 66. [3]
(a) Calculate the mean
(b) Find the median and mode
(c) Calculate the range
2. The frequency table below shows heights of 20 students. [3]
| Height (cm) |
150-159 |
160-169 |
170-179 |
180-189 |
| Frequency |
3 |
8 |
7 |
2 |
Calculate the estimated mean height.
3. Two datasets have the same mean of 50, but Dataset A has a range of 10 and Dataset B has a range of 50. [2]
Which dataset is more dispersed? Explain your answer.
Section B: Probability
4. A bag contains 5 red balls, 3 blue balls, and 2 green balls. A ball is drawn at random. [3]
(a) What is the probability of drawing a red ball?
(b) What is the probability of drawing a ball that is not blue?
(c) If a red ball is drawn and not replaced, what is the probability that the second ball is also red?
5. A fair coin is flipped 3 times. [3]
(a) List all possible outcomes
(b) What is the probability of getting exactly 2 heads?
(c) What is the probability of getting at least one tail?
6. Two events A and B are independent. P(A) = 0.3 and P(B) = 0.4. [2]
(a) Find P(A and B)
(b) Find P(A or B)
Section C: Problem Solving
7. In a class of 30 students, 18 study French and 15 study Spanish. 8 students study both languages. [3]
(a) How many students study only French?
(b) How many students study neither language?
(c) If a student is randomly selected, what is the probability they study Spanish?
8. A survey of 100 customers found that 60% prefer product A, 30% prefer product B, and 10% have no preference. If 20 more customers are surveyed and show the same distribution, what will be the new total preferring product A? [2]
Total marks: 24
Mark Scheme
1. (a) Mean = 599/10 = 59.9 [1]
(b) Median = (59 + 61)/2 = 60; No mode (or bimodal) [1]
(c) Range = 74 - 45 = 29 [1]
2. Estimated mean = (3×154.5 + 8×164.5 + 7×174.5 + 2×184.5)/20 [1]
= (463.5 + 1316 + 1221.5 + 369)/20 = 3370/20 = 168.5 cm [2]
3. Dataset B is more dispersed because it has a larger range [1]
The range is a measure of spread/dispersion [1]
4. (a) P(red) = 5/10 = 0.5 or 1/2 [1]
(b) P(not blue) = (5+2)/10 = 7/10 = 0.7 [1]
(c) P(second red | first red drawn) = 4/9 [1]
5. (a) HHH, HHT, HTH, HTT, THH, THT, TTH, TTT [1]
(b) P(exactly 2 heads) = 3/8 [1]
(c) P(at least 1 tail) = 7/8 [1]
6. (a) P(A and B) = 0.3 × 0.4 = 0.12 [1]
(b) P(A or B) = 0.3 + 0.4 - 0.12 = 0.58 [1]
7. (a) Only French = 18 - 8 = 10 [1]
(b) Neither = 30 - (18 + 15 - 8) = 30 - 25 = 5 [1]
(c) P(Spanish) = 15/30 = 0.5 [1]
8. Total customers = 120; preferring A = 0.6 × 120 = 72 [2]