# Measures of Location and Spread

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

#### Prerequisite Knowledge

• 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.

#### Success Criteria

• 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.

#### Key Concepts

• 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.

#### Common Misconceptions

• 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

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