Be able to recognise and work with categorical, discrete, continuous and ranked data. Be able to interpret standard diagrams for grouped and ungrouped single-variable data.

Includes knowing this vocabulary and deciding what data presentation methods are appropriate: bar chart, dot plot, histogram, vertical line chart, pie chart, stem-and-leaf diagram, box-and-whisker diagram (box plot), frequency chart.
Learners may be asked to add to diagrams in examinations in order to interpret data.

Notation: A frequency chart resembles a histogram with equal width bars but its vertical axis is frequency. A dot plot is similar to a bar chart but with stacks of dots in lines to represent frequency.

[Excludes: Comparative pie charts with area proportional to frequency.]

Histograms and frequency polygons Box and whisker plots

Understand that the area of each bar in a histogram is proportional to frequency. Be able to calculate proportions from a histogram and understand them in terms of estimated probabilities.

Includes use of area scale and calculation of frequency from frequency density.

Histograms and frequency polygons

Be able to interpret a cumulative frequency diagram.

Cumulative frequency diagrams

Be able to describe frequency distributions.

Symmetrical, unimodal, bimodal, skewed (positively and negatively).

[Excludes: Measures of skewness.]

Understand that diagrams representing unbiased samples become more representative of theoretical probability distributions with increasing sample size.

e.g. A bar chart representing the proportion of heads and tails when a fair coin is tossed tends to have the proportion of heads increasingly close to 50% as the sample size increases.

Be able to interpret a scatter diagram for bivariate data, interpret a regression line or other best fit model, including interpolation and extrapolation, understanding that extrapolation might not be justified.

Including the terms association, correlation, regression line.
Leaners should be able to interpret other best fit models produced by software (e.g. a curve).
Learners may be asked to add to diagrams in examinations in order to interpret data.

[Excludes: Calculation of equation of regression line from data or summary statistics.]

Scatter graphs

Be able to recognise when a scatter diagram appears to show distinct sections in the population. Be able to recognise and comment on outliers in a scatter diagram.

An outlier is an item which is inconsistent with the rest of the data.
Outliers in scatter diagrams should be judged by eye.

Scatter graphs

Be able to recognise and describe correlation in a scatter diagram and understand that correlation does not imply causation.

Positive correlation, negative correlation, no correlation, weak/strong correlation.

Correlation

Be able to select or critique data presentation techniques in the context of a statistical problem.

Including graphs for time series.

Select or critique data presentation techniques

Know the standard measures of central tendency and be able to calculate and interpret them and to decide when it is most appropriate to use one of them.

Median, mode, (arithmetic) mean, midrange. The main focus of questions will be on interpretation rather than calculation.
Includes understanding when it is appropriate to use a weighted mean e.g. when using populations as weights.

Notation:
Mean \(= \bar{x}\)

Mean, mode and median

Know simple measures of spread and be able to use and interpret them appropriately.

Range, percentiles, quartiles, interquartile range.

Range and interquartile range

Know how to calculate and interpret variance and standard deviation for raw data, frequency distributions, grouped frequency distributions.
Be able to use the statistical functions of a calculator to find mean and standard deviation.

sample variance: \(s^2 = \dfrac{S_{xx}}{n-1}\)

where \(S_{xx} = \displaystyle\sum_{i=1}^n{(x_i-\bar{x})^2}\)

sample standard deviation: \(s = \sqrt{\text{variance}} \)

[Excludes:Corrections for class interval in these calculations.]

Variance and standard deviation Coding data

Understand the term outlier and be able to identify outliers. Know that the term outlier can be applied to an item of data which is:
• at least 2 standard deviations from the mean;
OR
• at least \(1.5 × IQR\) beyond the nearer quartile.

An outlier is an item which is inconsistent with the rest of the data.

Outliers and cleaning data

Be able to clean data including dealing with missing data, errors and outliers.

Outliers and cleaning data