Edexcel 4MA1Cambridge 0580
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Edexcel IGCSE Maths A (4MA1) · Foundation tier · Revision notes

IGCSE Maths 4MA1 Foundation Statistics and Probability Notes

Revision notes for statistics and probability at Foundation tier (Papers 1F and 2F, grades 5 to 1). Each sub-topic has what you need to know, the key methods, a common mistake and a worked example. Cover the worked solution and try the example first.

Statistics and Probability questions with answers →

6.1 Graphical representation of data

What you need to know: pictograms, bar charts, pie charts and two-way tables.

  • A pictogram needs a key showing what one symbol represents.
  • In a pie chart, each item gets 360° ÷ total; multiply by its frequency to get its angle.
  • A two-way table shows two kinds of information; the rows and columns add up to the totals.
  • When you compare pie charts, remember they show proportions, not the actual numbers.

Watch out: Check that your pie chart angles add up to 360°.

Worked example (3 marks, grade 3):

40 people chose their favourite drink: tea 14, coffee 18, juice 8.

Work out the angle for each sector of a pie chart to show this information.

  1. Each person is 360 ÷ 40 = 9°.
  2. Tea: 14 × 9 = 126°. Coffee: 18 × 9 = 162°. Juice: 8 × 9 = 72°. (Check: 126 + 162 + 72 = 360.)

Answer: tea \(126°\), coffee \(162°\), juice \(72°\)

Higher tier only: histograms with unequal class widths and cumulative frequency diagrams.

Practise: Graphical representation of data questions with answers · Unit 6 practice (Foundation) · Higher level: Histograms and Cumulative Frequency questions

6.2 Statistical measures

What you need to know: mean, median, mode and range; averages from tables; estimated mean and modal class of grouped data.

  • Mean = total ÷ number of values; the median is the middle value once the values are in order; the mode is the most common value; range = largest − smallest.
  • From a frequency table, the total is the sum of value × frequency.
  • For grouped data, estimate the mean with the midpoint of each class; the modal class has the highest frequency.
  • Compare data sets with an average and a measure of spread such as the range.

Watch out: Put the values in order before finding the median.

Worked example (4 marks, grade 3):

The table shows the number of goals scored in 20 matches.

Goals: 0, 1, 2, 3, 4

Frequency: 4, 7, 6, 2, 1

Find (a) the mode (b) the median (c) the mean number of goals.

  1. (a) 1 goal has the highest frequency (7).
  2. (b) The median is between the 10th and 11th values. The first 4 are 0 and the next 7 (5th to 11th) are 1, so the median is 1.
  3. (c) Total goals = 0 + 7 + 12 + 6 + 4 = 29; mean = 29 ÷ 20 = 1.45.

Answer: (a) \(1\) (b) \(1\) (c) \(1.45\)

Higher tier only: medians and quartiles from cumulative frequency, interquartile range.

Practise: Statistical measures questions with answers · Unit 6 practice (Foundation) · Higher level: Mean, Median and Mode questions

6.3 Probability

What you need to know: the probability scale; theoretical and experimental probability; sample spaces and Venn diagrams; P(not A), mutually exclusive events and expected frequency.

  • Probabilities run from 0 (impossible) to 1 (certain); P(event) = number of ways it can happen ÷ number of equally likely outcomes.
  • P(not A) = 1 − P(A), and for mutually exclusive events P(A or B) = P(A) + P(B).
  • List the outcomes of two events systematically, or use a sample space diagram.
  • Relative frequency = number of times it happened ÷ number of trials; expected frequency = probability × number of trials.

Watch out: The probabilities of all the possible outcomes add up to 1.

Worked example (2 marks, grade 3):

A bag holds one red ball (R) and one blue ball (B). Zara takes a ball at random, puts it back, then takes a ball at random again.

(a) List all the possible outcomes.

(b) Find the probability that both balls are the same colour.

  1. (a) List systematically: first ball R then B, each with the second ball R or B.
  2. (b) Same colour: RR and BB, 2 out of 4 = 1/2.

Answer: (a) RR, RB, BR, BB (b) \(\frac{1}{2}\)

Higher tier only: tree diagrams, independent events and conditional probability.

Practise: Probability questions with answers · Unit 6 practice (Foundation) · Higher level: Sets and Venn Diagrams questions · Probability questions

Topic list for Edexcel IGCSE Maths 4MA1 Foundation statistics and probability: graphical representation of data, statistical measures, probability
The 3 Foundation sub-topics of statistics and probability.

Practise statistics and probability