Grade 12 Statistics Calculator

Free Grade 12 statistics calculator for CAPS Maths: mean, median, standard deviation, quartiles and variance from a data set.

Paste or type your data values separated by commas or spaces. The calculator returns the full five-number summary plus the mean, variance and population standard deviation used in CAPS. In the exam you use your calculator's statistics mode for the mean and standard deviation, so this tool is best for checking answers and seeing how each value is built. Interpretation still earns marks: say what the spread or skewness means in the context of the data.

How it works

  • Values are sorted to find the median and the lower and upper quartiles.
  • The mean is Σx / n and the variance is Σ(x − x̄)² / n.
  • Standard deviation is the square root of the variance (population formula, as used in CAPS).
  • An outlier pulls the mean and standard deviation towards it but has little effect on the median and quartiles.
  • Worked example: for 3, 5, 7, 8, 9, 11, 12, 15 the mean is 70 ÷ 8 = 8.75, the median is 8.5, Q1 = 6 and Q3 = 11.5, so the interquartile range is 5.5.

Frequently asked questions

Does this use the population or sample standard deviation?

The population formula (divide by n), which is what the CAPS Grade 12 curriculum and NSC memos use.

How are quartiles calculated?

The data is split at the median, and Q1 and Q3 are the medians of the lower and upper halves.

What does the standard deviation tell me?

How spread out the data is around the mean. A small standard deviation means most values are close to the mean; a large one means they are widely spread.

How do I count values within one standard deviation of the mean?

Work out the interval from x̄ − σ to x̄ + σ, then count the data values inside it. NSC questions often ask for this number or as a percentage of the data.

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