---
title: "Data: cheat sheet"
subtitle: "Data and chance"
---

# Data

> The words and methods from this unit, with an example of each.

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**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.

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

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

$$\text{mean} = \dfrac{\text{total}}{\text{number of values}} = \dfrac{30}{5} = 6$$

_3, 5, 5, 6, 11: mean 6 (▲), median 5 (dashed)_

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

$$3, 4, \underline{6, 7}, 8, 9 \to \tfrac{6 + 7}{2} = 6.5$$

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

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

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**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.

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

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**stem-and-leaf plot**: Tens as stems, units as leaves in order; include every stem, even with no leaves; give a key.

$$3 \mid 1\ 5\ 5\ 8 = 31, 35, 35, 38$$

_Stems are the tens, leaves the units_

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

$$\text{centre } (15, 16) \text{ and spread } (6, 16)$$

_Similar medians; Class B much more spread_

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**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.

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

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