Mathematics
Statistics and probability — Topics 8-9
- 1.
The values 2, 4, 6 and 8 have frequencies 3, 5, 4 and 2 respectively. Calculate the mean.
[4 marks] - 2.
A bag contains 5 red and 3 blue counters. Two counters are taken without replacement. Calculate the probability that both are blue.
[4 marks] · no calculator - 3.
Find the median and interquartile range of the data set: 3, 7, 8, 12, 14, 15, 19, 22.
[4 marks] · no calculator - 4.
A fair six-sided die is rolled twice. Calculate the probability that the sum of the two scores is 9.
[3 marks] · no calculator - 5.
A survey of 50 students recorded the number of siblings each has, shown in a frequency table: 0 siblings (12 students), 1 sibling (20), 2 siblings (13), 3 siblings (5). Calculate the mean number of siblings.
[3 marks] - 6.
Two events A and B are independent, with P(A) = 0.3 and P(B) = 0.5. Calculate P(A and B) and P(A or B).
[4 marks] - 7.
A cumulative frequency curve for 80 students' test scores shows that the median score is 62 and the 90th percentile is 85. Interpret what the 90th percentile value tells you about the distribution of scores.
[2 marks] · no calculator - 8.
A box contains 4 red pens and 6 blue pens. A pen is chosen at random, its colour noted, and it is replaced before a second pen is chosen. Draw a tree diagram outcome summary and calculate the probability that both pens are the same colour.
[4 marks] - 9.
A set of 6 numbers has mean 10. A seventh number, 24, is added to the set. Calculate the new mean.
[3 marks] - 10.
Explain why the mode is a more appropriate average than the mean for a data set that includes categorical data such as favourite colour.
[2 marks] · no calculator - 11.
The table shows the time (in minutes) taken by 40 students to complete a puzzle: 0 < t ≤ 10 (8 students), 10 < t ≤ 20 (15), 20 < t ≤ 30 (12), 30 < t ≤ 40 (5). Calculate an estimate of the mean time, using the midpoint of each interval.
[4 marks] - 12.
A histogram has a bar covering the class interval 10 to 25 (a width of 15), with a frequency density of 2.4. Calculate the frequency for this class interval.
[3 marks] - 13.
In a class of 30 students, 18 study French, 15 study Spanish, and 8 study both. Calculate the number of students who study neither language.
[3 marks] - 14.
Using the class in the previous question (18 study French, 15 study Spanish, 8 study both), a student is selected at random from those who study French. Calculate the probability that this student also studies Spanish.
[2 marks] · no calculator - 15.
A biased coin is thrown 200 times and lands on heads 140 times. (a) Calculate the relative frequency of heads. (b) State the best estimate of the probability that the next throw lands on heads.
[2 marks] - 16.
A cumulative frequency table for the number of books read by 60 students in a year shows: ≤5 books (10 students), ≤10 books (28), ≤15 books (48), ≤20 books (60). Use linear interpolation to estimate the median number of books read.
[4 marks] - 17.
A survey of 60 people recorded whether they like a sport and their gender: 24 males like it, 6 males dislike it, 18 females like it, 12 females dislike it. Calculate the probability that a randomly selected person from the survey is female and likes the sport.
[3 marks] - 18.
A bag contains 4 green and 6 yellow balls. Three balls are drawn at random without replacement. Calculate the probability that all three balls are yellow.
[3 marks] - 19.
A scatter diagram shows a strong positive correlation between hours studied and exam score, based on data for students who studied between 2 and 10 hours. State what a strong positive correlation means, and explain one reason it would be unreliable to use the line of best fit to predict the score for a student who studied 25 hours.
[2 marks] · no calculator - 20.
A box-and-whisker plot has minimum 4, lower quartile 10, median 15, upper quartile 22, and maximum 30. Calculate the interquartile range, and state whether a new value of 35 could belong to this same data set, giving a reason.
[2 marks] · no calculator - 21.
A bag contains three red and two blue counters. Two are drawn without replacement. Find the probability that both are red.
[3 marks] · no calculator - 22.
A bag contains four red and three blue counters. Two are drawn without replacement. Given that at least one is blue, find the probability that both are blue.
[5 marks] · no calculator