Year 8 Probability and statistics: revision mind map

1Interpreting graphs and tables

Read the title, the axes, the scale and the key first.

Column graphs for categories, line graphs for change over time, pie charts for parts of a whole

2Frequency tables

Tally each result, then count. Frequency is how many times it happened.

5 out of 20 results: relative frequency $\tfrac{5}{20} = 25\%$

3Graphs of frequency tables

Histograms show numerical data: the columns touch.

Also: dot plots, and stem-and-leaf plots (key 2 | 4 = 24)

4Measures of centre

Mean: add and divide. Median: middle value in order. Mode: most common.

1, 3, 3, 6, 7: mean $\tfrac{20}{5} = 4$, median 3, mode 3

2, 4, 6, 9: median $\tfrac{4 + 6}{2} = 5$

5Measures of spread

Range = max − min. IQR $= Q_3 - Q_1$, the spread of the middle half.

2, 4, 5, 7, 8, 10: range $8$

$Q_1 = 4,\ Q_3 = 8$, so IQR $= 4$

Split the data in half at the median, then find the median of each half.

6Surveying and sampling

A sample should represent the population. Random samples avoid bias.

Census: everyone. Sample: some

Asking only your friends isn't a random sample

7Probability

$P = \dfrac{\text{favourable}}{\text{total}}$, from 0 (impossible) to 1 (certain).

One die: $P(5 \text{ or } 6) = \tfrac26 = \tfrac13$

$P(\text{not } 6) = 1 - \tfrac16 = \tfrac56$

8Two-step experiments

List every outcome in a table.

Two coins: HH, HT, TH, TT. $P(\text{one head}) = \tfrac24 = \tfrac12$

Two dice: $P(\text{sum of } 12) = \tfrac{1}{36}$

9Tree diagrams

Multiply along the branches, then add the results you want.

3 red and 1 blue, with replacement: $P(\text{red, red}) = \tfrac34 \times \tfrac34 = \tfrac{9}{16}$

10Venn diagrams and two-way tables

Fill in the overlap first.

25 people: $P(\text{both}) = \tfrac{4}{25}$

11Experimental probability

Relative frequency $= \dfrac{\text{times it happened}}{\text{number of trials}}$

18 heads in 50 tosses: $\tfrac{18}{50} = 0.36$. The expected probability is 0.5.

More trials usually get closer to the expected probability.