Collect and display data, find its centre and spread, and compare data sets; then list what can happen, give it a probability, and test it with experiments.
Counting and measuring, mean, median, mode and range, stem-and-leaf plots, and comparing two data sets.
Numerical data is discrete when it is counted (siblings: 0, 1, 2, …) and continuous when it is measured (a 100 m time can be any value, such as 14.37 s). Measured values are always rounded to some precision.
Four numbers that sum up a data set: the mean (add, then share equally), the median (the middle value once sorted), the mode (the most common) and the range (highest minus lowest).
Choose the measure that tells the truth about the data. An outlier drags the mean, so the median is better for data with extreme values; the mean uses every value when there are none; the mode suits the most common choice.
A stem-and-leaf plot keeps every value and shows the shape: the tens are the stems, the units are the leaves, written in order. Include every stem, even with no leaves, and add a key.
Describe a data set by its shape (symmetrical or skewed, with clusters, gaps or outliers), its centre and its spread. Compare two sets on centre and spread, with numbers and in context, not by one value.
An investigation asks a question that data can answer, plans who to measure and how, collects and displays the data, describes its shape, centre and spread, and reports an answer with its limits.
Sample spaces and probabilities, then experiments: what happens in 10 trials, and in 1000. Year 8: complements, Venn diagrams, two-way tables, grids and trees, and, or, not, and simulations.
The sample space lists every possible outcome. When the outcomes are equally likely, the probability of an event is favourable outcomes ÷ total outcomes; when they are not (a spinner with a bigger sector), use the sizes. The probabilities add to 1.
The expected number of times an outcome happens is its probability × the number of trials: 60 rolls should give about 10 sixes. Run the experiment and record the counts: the results come close, but rarely exactly.
Over a few trials the relative frequency jumps about; over many it settles close to the probability. That is why more trials give a better estimate, and why a run of tails does not make heads 'due'.
An event and its complement (everything else that could happen) cover every outcome once. Use that to find probabilities quickly, especially for 'at least one'.
When everyone in a group is sorted by two yes/no questions, a Venn diagram and a two-way table show the same four groups: one, the other, both and neither. Each person is in exactly one of them.
Two events, one after the other, make a sample space of pairs. A grid or a tree diagram lists every pair once, so you can count the outcomes in an event and find its probability.
'A and B' means both happen; 'A or B' means at least one happens (both included); 'not A' is everything else. Read them from a Venn diagram, a two-way table or a grid, counting each outcome once.
A computer can repeat a chance experiment thousands of times in a second. Run a simulation of two events, record the results in a frequency table, and compare the relative frequency with the probability from the sample space.
Year 8: census, sample, experiment and observation; bias; ways to choose a sample; describing a sample; how samples vary; and investigations that infer about a population.
Data can come from everyone (a census), from some (a sample), from an experiment where you change something on purpose, or from watching (an observation). Each has a cost, a time and an accuracy; choose the one that fits the question.
Bias is anything in the way data is collected that pushes the result one way. It can come from who is asked, how they are asked, or how things are measured, and a bigger sample does not fix it.
A sample can be chosen at random, every so many people on a list, a fair share from each group, or whoever is easiest to reach. Random ways give every member a chance; the easy way is often biased.
Display a sample's data, then report its shape, centre and spread, and what it suggests about the population: an estimate, with the sampling method and size stated.
Random samples from the same population give different results. That is sampling variation, not a mistake. Bigger samples vary less, so their results are more reliable.
A sample investigation asks a question about a population, plans a fair and ethical sample, collects and describes the data, then makes an inference about the population and says how sure it can be.
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