Measures of Location and Spread

Scheme of work: Year 12 A-Level: Applied: Statistics: Measures of Location and Spread

Use the mode, mean and median to interpret, analyse and compare the distributions of data sets
Use the range and interquartile range to interpret, analyse and compare the spread of data sets.

Calculate measures of location, mean, median and mode;
Recognise when each measure of location is most suitable;
Calculate measures of variation, standard deviation, variance, range and interpercentile range;
Interpret and draw inferences from summary statistics.

Students need to be able to calculate the mean, variation, and standard deviation from a dataset using the Statistics mode on a calculator.
A measure of location tells you roughly where the centre of data lies. Dispersion tells you how spread out the data is.
Students should be familiar with the different formulae for working out variation.
When using the median, students should use the interquartile range as the measure of spread. When using the mean, the measure of spread is variance and standard deviation.
Students need to be familiar with the different methods for finding the measures of location for discrete and continuous data. Interpolation is used for continuous data.
Students should be precise when referring to location and central tendency measures. For instance, refer to the ‘median’ rather than average or ‘interquartile range’ rather than spread.

When calculating the mean of grouped data, some students may divide by the number of groups rather than the number of data items.
When finding the standard deviation, students forget to take the square root.
Some students waste time by ignoring given values and recalculating ∑fx and ∑fx².
Students often forget about the effect that coding data has on the variance.
Students often forget to calculate the mean and standard deviation of grouped data using the statistics mode on their calculator and prefer to work it out