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LearnEdexcel4MA12016 specificationPapers 1H, 2H · Higher tierStatistics and probability

Papers 1H, 2H · Module

Statistics and probability

8 subtopics≈ 235 min in total

Start the module: Collecting data and stem-and-leaf diagrams Open graphing calculator

Collecting data and stem-and-leaf diagrams
Data is qualitative (words) or quantitative (numbers); numbers are discrete (counted) or continuous (measured). A fair sample represents the whole population without bias. Frequency tables and stem-and-leaf diagrams organise raw data so you can read off the median, mode and range.
≈ 25 min
Averages and range
The mean shares the total equally, the median is the middle value in order, and the mode is the most common. The range measures spread. For frequency tables, multiply each value by its frequency; for grouped data, use the class midpoints.
≈ 30 min
Charts, tables and scatter diagrams
A pie chart shares $360^\circ$ in proportion to the frequencies. A two-way table splits a group by two features at once. A scatter diagram shows whether two quantities are related, and a line of best fit lets you estimate one from the other within the range of the data.
≈ 30 min
Cumulative frequency
Cumulative frequency is a running total. Plot it against the upper class boundaries and join the points to get an S-shaped curve. Read across at $\tfrac n2$ for the median, and at $\tfrac n4$ and $\tfrac{3n}4$ for the quartiles. The interquartile range is the spread of the middle half.
≈ 30 min
Histograms
In a histogram, the area of each bar shows the frequency. When classes have different widths, the height is the frequency density: frequency ÷ class width. To read a frequency back, multiply density by width.
≈ 30 min
Single events and relative frequency
When outcomes are equally likely, probability $=\dfrac{\text{favourable outcomes}}{\text{total outcomes}}$ . The probabilities of all outcomes add to $1$ , so $P(\text{not }A)=1-P(A)$ . When you can't count outcomes, estimate the probability from experiments: relative frequency.
≈ 25 min
Combined events and tree diagrams
For two independent events, multiply ("and"). For mutually exclusive outcomes, add ("or"). A tree diagram organises both: multiply along each route, then add the routes you want. For "at least one", use $1-P(\text{none})$ .
≈ 35 min
Without replacement and Venn diagrams
When an item is not put back, the second pick has one fewer item, and possibly one fewer of the colour you took. A Venn diagram sorts a group into "only $A$ ", "both", "only $B$ " and "neither": fill in the overlap first.
≈ 30 min