Statistics

📌 Key points

1. Discrete data can only take certain values (e.g. number of goals); continuous data can take any value in a range (e.g. time, height).
2. Mean = total of valuesnumber of values; median = the middle value when the data are in order; mode = the most common value; range = largest − smallest.
3. From a frequency table, mean = ΣfxΣf. For grouped data use the midpoint of each class, so the mean is only an estimate.
4. Pie chart angle = frequencytotal × 360°. Stem-and-leaf diagrams must have a key, e.g. 3 | 4 means 34.
5. Scatter diagrams show positive, negative or no correlation. A line of best fit can estimate values inside the data range; predicting far outside it (extrapolation) is unreliable.
6. Cumulative frequency: plot at the upper end of each class. For n values, read the median at n2, the lower quartile at n4 and the upper quartile at 3n4.
7. Interquartile range (IQR) = upper quartile − lower quartile; it measures the spread of the middle half of the data.
8. Histograms: frequency density = frequencyclass width. The area of each bar shows the frequency.
9. To compare two distributions, compare an average (e.g. median) and a measure of spread (e.g. IQR or range), in context.

📖 Key terms

Discrete data

Data that can only take particular values, usually counted.

Continuous data

Data that can take any value in a range, usually measured.

Mode

The most common value.

Median

The middle value when the data are in order.

Range

Largest value − smallest value.

Interquartile range

Upper quartile − lower quartile.

Frequency density

Frequency ÷ class width; the height of a histogram bar.

Correlation

The relationship between two variables shown on a scatter diagram.