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Data: cheat sheet

Data and chance · The words and methods from the lessons, with an example of each.

discrete and continuous

Discrete data takes separate values (number of siblings). Continuous data can be any value in a range (height, time), and is rounded when recorded.

counted: discretemeasured: continuous\text{counted: discrete} \quad \text{measured: continuous}

median

Sort first; the middle value, or halfway between the two middle values for an even count.

3,4,6,7‾,8,9→6+72=6.53, 4, \underline{6, 7}, 8, 9 \to \tfrac{6 + 7}{2} = 6.5

mode and range

There can be two modes, or none. The range is a simple measure of spread.

mode: most commonrange=highest−lowest\text{mode: most common} \quad \text{range} = \text{highest} - \text{lowest}

stem-and-leaf plot

Tens as stems, units as leaves in order; include every stem, even with no leaves; give a key.

3∣1 5 5 8=31,35,35,383 \mid 1\ 5\ 5\ 8 = 31, 35, 35, 38
Stems are the tens, leaves the units
Stems are the tens, leaves the units

statistical investigation

Ask a question data can answer, plan the variable and a fair sample, collect and display the data, describe its shape, centre and spread, then report the answer with its limits.

ask→plan→collect→display→summarise→report\text{ask} \to \text{plan} \to \text{collect} \to \text{display} \to \text{summarise} \to \text{report}

mean

Add the values, then share equally. An outlier pulls the mean towards it.

mean=totalnumber of values=305=6\text{mean} = \dfrac{\text{total}}{\text{number of values}} = \dfrac{30}{5} = 6
3, 5, 5, 6, 11: mean 6 (▲), median 5 (dashed)
3, 5, 5, 6, 11: mean 6 (▲), median 5 (dashed)

choosing a measure

With an outlier, the median describes a typical value better than the mean. Without, the mean uses every value. For 'most common', use the mode.

5,6,6,7,8,40: median 6.55, 6, 6, 7, 8, \mathbf{40}:\ \text{median } 6.5

comparing data sets

Describe shape (symmetrical or skewed, clusters, gaps, outliers), centre and spread. Compare both centre and spread, with numbers, in context.

centre (15,16) and spread (6,16)\text{centre } (15, 16) \text{ and spread } (6, 16)
Similar medians; Class B much more spread
Similar medians; Class B much more spread