Year 10 Statistics: revision mind map

1Collecting representative data

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

Census: everyone. Sample: some

Random, systematic or stratified sampling

2Data displays

Histograms for numerical data, column graphs for categories.

Shape: symmetric, positively skewed (tail to the right), negatively skewed, bimodal

3Two-way tables

Count by two categories, then use the row and column totals.

25 of 40 students play sport; 15 of those are in Year 10

$\tfrac{15}{25} = 60\%$ of the sport players are in Year 10

4Summary statistics

Centre: mean and median. Spread: range and IQR.

4, 6, 7, 9, 14: mean $\tfrac{40}{5} = 8$, median 7

An outlier pulls the mean, not the median.

5Box plots and outliers

Outlier: below $Q_1 - 1.5 \times \text{IQR}$ or above $Q_3 + 1.5 \times \text{IQR}$.

$Q_1 = 10,\ Q_3 = 18$: IQR 8, upper fence $18 + 12 = 30$, so 34 is an outlier

6Standard deviation

Standard deviation $\sigma$ measures spread around the mean. Small $\sigma$: data close to the mean.

Bell-shaped data: about 68% within $1\sigma$, 95% within $2\sigma$

Mean 70, $\sigma = 5$: about 95% between 60 and 80

7Cumulative frequency and percentiles

Cumulative frequency is a running total. Read percentiles off the graph (ogive).

Median = 50th percentile, Q₁ = 25th, Q₃ = 75th

40 values: the median is halfway between the 20th and 21st

8Time-series data

Data collected over time, with time on the x-axis.

Look for the trend (up or down) and any seasonal pattern

9Bivariate data and scatter plots

Two numerical variables: explanatory on the x-axis, response on the y-axis.

Describe the direction (positive or negative), strength and form (linear or not)

Watch out: correlation doesn't prove that one causes the other.

10Line of best fit

Draw it by eye with about the same number of points on each side.

$y = 2.5x + 10$ at $x = 8$: $y = 30$

Predicting inside the data (interpolation) is more reliable than outside it