Interpret measures of central tendency and variation, extending to…

The idea

Measures of central tendency, such as the mean, median and mode, describe a typical value, while measures of variation, such as range, interquartile range and standard deviation, describe spread. Standard deviation measures how far values typically lie from the mean, in the same units as the data. For this specification, standard deviation uses division by n. From summary statistics, use the formula standard deviation equals the square root of the quantity (sum of x squared divided by n) minus the mean squared. For example, if sum of x = 20, sum of x squared = 130, and n = 5, the mean is 4 and standard deviation is sqrt(130/5 - 16) = sqrt(26 - 16) = sqrt(10) = 3.16. Interpret a larger standard deviation as greater spread about the mean.

What earns the marks

• Distinguishes measures of central tendency from measures of variation and states what each describes.
• Calculates a mean from raw data or summary totals and uses it in further work.
• Applies the standard deviation formula, ensuring division by n as required by the specification.
• Uses summary statistics such as sum of x, sum of x squared and n to find a standard deviation without the raw data.
• Interprets standard deviation as a measure of spread in the original units and compares two data sets using it.

Common mistakes and how to put them right

• Dividing by n minus 1 instead of n when calculating standard deviation.

  Put it right by dividing by n for standard deviation in this specification.

• Forgetting to take the square root at the end of the calculation.

  Put it right: Take the square root of the variance to obtain the standard deviation.

• Mixing up sum of x squared with the square of sum of x.

  Put it right: Keep the two summary quantities distinct and use the correct one in the formula.

Exam tips

• Write the formula you are using before substituting values, and keep the mean to full accuracy until the final rounding.
• Remember that standard deviation calculations in this specification always use division by n, not n minus 1.
• When comparing two data sets, quote both standard deviations and state which is more spread out in context.