Measures of Location and Spread

This lesson covers measures of central tendency (location) and measures of spread (dispersion) for the Edexcel A-Level Mathematics specification (9MA0), Paper 3 Section A -- Statistics. You must know how to calculate the mean, median, mode, range, IQR, variance, and standard deviation from raw data and from frequency tables, including how to work with coded data.

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Measures of Location (Central Tendency)

Mean

The mean (or arithmetic mean) is the sum of all the values divided by the number of values.

For raw data with n values x1, x2, ..., xn:

Mean (x-bar) = (x1 + x2 + ... + xn) / n

Using sigma notation: x-bar = (1/n) x Sigma(xi)

Mean from a frequency table

When data is presented in a frequency table:

Mean = Sigma(f x x) / Sigma(f)

where f is the frequency and x is the data value (or the midpoint of the class for grouped data).

Example (grouped data)