Probability and Data Handling
Probability and Data Handling covers the probability scale from 0 to 1, calculating the probability of a single event and relative frequency from experimental data, and handling data through averages and representations such as bar charts and pie charts.
Method
- Remember that probability is always written as a fraction, decimal or percentage between 0 (impossible) and 1 (certain).
- For a single event with equally likely outcomes, probability = number of favourable outcomes / total number of possible outcomes.
- List all possible outcomes systematically, for example using a list or a table, before calculating a probability, to avoid missing any.
- Remember that the probabilities of all possible outcomes for an event must add up to 1, so a missing probability can be found by subtracting the others from 1.
- For relative frequency, divide the number of times an event happened by the total number of trials; the more trials there are, the more reliable the estimate of the true probability.
- To find the mean, add all the values and divide by how many values there are; to find the median, put the values in order and find the middle one (or the average of the middle two); the mode is the most common value; the range is the largest value minus the smallest.
- When reading a pie chart, remember the whole circle represents 360 degrees or 100% of the data, so a sector's share can be found using its angle out of 360, or its percentage.
- When comparing two sets of data, compare both an average, to show a typical value, and the range or spread, to show consistency, rather than an average alone.
Worked example
A drawer contains 5 black socks, 3 grey socks and 2 white socks, all mixed together. A sock is picked at random. (a) Find the probability that it is grey. (b) Find the probability that it is not white.
- Find the total number of socks: 5 + 3 + 2 = 10.
- For part (a), the number of grey socks is 3, so the probability is 3/10.
- For part (b), find the probability of white first, 2/10, then subtract from 1, since 'not white' is the complement of 'white'.
- Calculate: 1 - 2/10 = 8/10 = 4/5. Final answer: P(grey) = 3/10, and P(not white) = 4/5.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A fair six-sided dice is rolled once. Find the probability of rolling a number greater than 4.Show answer
Answer: 1/3 (the numbers 5 and 6 are greater than 4, so 2 out of 6 outcomes: 2/6 = 1/3)
Q2A spinner has a probability of 0.3 of landing on red, a probability of 0.45 of landing on blue, and the remaining probability of landing on green. Find the probability of landing on green.Show answer
Answer: 0.25 (1 - 0.3 - 0.45 = 0.25)
Q3Find the mean of these test scores: 14, 18, 12, 20, 16.Show answer
Answer: 16 (14 + 18 + 12 + 20 + 16 = 80, then 80 / 5 = 16)
Q4Find the median and the range of this data set: 7, 3, 9, 3, 12, 5.Show answer
Answer: Median = 6 (order the data: 3, 3, 5, 7, 9, 12, then average the middle two, 5 and 7: (5 + 7) / 2 = 6); range = 9 (12 - 3 = 9)
Q5A survey of 40 students' favourite sport is shown in a pie chart. If football takes up a sector of 90 degrees, what percentage of students chose football?Show answer
Answer: 25% (90 / 360 = 1/4 = 25%)
Q6A coin is flipped 200 times and lands on heads 118 times. Calculate the relative frequency of landing on heads.Show answer
Answer: 0.59 (118 / 200 = 0.59)
Q7A bag contains only red and yellow beads. The probability of picking a red bead is 0.65. If there are 140 beads in total, how many are yellow?Show answer
Answer: 49 yellow beads (P(yellow) = 1 - 0.65 = 0.35, then 0.35 x 140 = 49)
Q8Two coins are flipped at the same time. List all the possible outcomes, and find the probability of getting exactly one head.Show answer
Answer: Outcomes: HH, HT, TH, TT; probability of exactly one head = 2/4 = 1/2 (HT and TH each have exactly one head)
Exam-style questions
Written in the style of a 13+ Common Entrance exam paper, with a full mark scheme.
A box contains 4 chocolate bars, 6 fruit bars and n cereal bars. The probability of picking a fruit bar at random is 0.3. (a) Find the total number of bars in the box. (b) Find the value of n.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A survey recorded how many books 10 students read over the summer holiday: 0 books read by 2 students, 1 book read by 3 students, 2 books read by 4 students, 3 books read by 1 student. Calculate (a) the mean number of books read per student, and (b) the mode.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
A survey asked 120 people which of three newspapers they read: The Herald, The Times, or The Courier. The results are shown in a pie chart: The Herald has a sector angle of 150 degrees, The Times has a sector angle of 120 degrees, and the rest read The Courier. (a) Calculate the number of people who read The Herald. (b) Calculate the number of people who read The Courier.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
Free printable worksheet
Want more practice on paper? Download the probability and data handling worksheet pack - 13 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 21 of 13+ Maths Workbook, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on probability and data handling, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.