StatisticsQ&A by dot point

Calculate the mean, median and mode, find a weighted mean and the mean from a frequency or grouped frequency table, identify the modal class, and choose the most appropriate average for the data.

Find the range, quartiles, interquartile range and percentiles, calculate the standard deviation, identify outliers, and draw and compare box plots of two distributions.

Calculate and interpret standardised scores using the mean and standard deviation to compare values across different distributions, and describe the skewness of a distribution.

Classify data as qualitative or quantitative, discrete or continuous, primary or secondary, and design good questionnaires, data-collection sheets and surveys that avoid bias and leading questions.

Understand sampling frames and choose between random, systematic, stratified, quota, cluster and convenience sampling, including how each is carried out and the bias each can introduce.

Calculate theoretical and experimental probability and relative frequency, use sample spaces, apply the addition law for mutually exclusive events and the multiplication law for independent events, use tree and Venn diagrams, and find expected frequency.

Construct and interpret frequency tables, two-way tables, pictograms, bar charts (including composite and comparative), pie charts and stem-and-leaf diagrams, choosing the correct display for the type of data.

Construct and interpret frequency polygons, histograms with equal and unequal class widths using frequency density, and cumulative frequency curves, and read the median and quartiles from a cumulative frequency curve.

Understand quality assurance and use control charts for the sample mean and range, interpreting warning and action limits to decide when a process is in control or needs adjusting.

Draw and interpret scatter diagrams, describe correlation, use a line of best fit to estimate values (interpolation and extrapolation), understand that correlation does not imply causation, and calculate and interpret Spearman's rank correlation coefficient.

Understand the properties of the normal distribution, use the 68 to 95 to 99.7 rule about the mean and standard deviation, and use standardised scores to compare and find proportions of normally distributed data.

Understand and use the statistical enquiry cycle: specify the problem and plan, collect the data, process and represent the data, then interpret and discuss the results, choosing methods that fit the hypothesis.

Calculate and interpret simple index numbers, understand the Retail Prices Index and Consumer Prices Index, find a weighted index number, and use a chain base to compare year-on-year change.

Plot and interpret a time series, calculate moving averages to smooth the data, plot and use a trend line, identify seasonal variation, and use the trend to make predictions.