Grade 11 Statistics

Grade 11 statistics: histograms, frequency polygons, ogives, variance, standard deviation, skewness and outliers, with worked CAPS examples and…

Statistics is about 20 of the 150 marks in Grade 11 Paper 2. You represent grouped data with histograms, frequency polygons and ogives (cumulative frequency curves), and read the median and quartiles from an ogive.

Grade 11 also introduces variance and standard deviation, which measure how far the data spreads from the mean, and asks you to describe data as symmetric or skewed and to identify outliers. Grade 12 adds scatter plots, regression and correlation.

Key concepts

  • Histograms and frequency polygons for grouped data
  • Ogives: plot cumulative frequency against the upper class boundary
  • Reading the median and quartiles from an ogive
  • Variance σ² = Σ(x − x̄)² / n and standard deviation σ = √σ²
  • Symmetric, positively skewed and negatively skewed distributions
  • Outliers: values far from the rest, e.g. beyond Q3 + 1.5 × IQR

Worked examples

Find the standard deviation of 2; 4; 6; 8; 10.

The mean is 6. Squared deviations: 16 + 4 + 0 + 4 + 16 = 40. Variance = 40 ÷ 5 = 8, so σ = √8 ≈ 2.83.

In a distribution the mean is greater than the median. How is it skewed?

A tail of high values pulls the mean above the median, so the data is positively (right) skewed.

Data has Q1 = 20 and Q3 = 30. Is 48 an outlier?

IQR = 10. Q3 + 1.5 × IQR = 30 + 15 = 45. Since 48 > 45, it is an outlier.

An ogive shows a total frequency of 80. How do you read the median from it?

The median is the value at half the total frequency. Draw a line across from 40 on the cumulative frequency axis to the curve, then down to read the value.

Common mistakes

  • Plotting an ogive at the class midpoints instead of the upper class boundaries.
  • Using n − 1 instead of n for standard deviation (CAPS uses the population formula, dividing by n).
  • Saying data is skewed towards the side where most values are, instead of the side of the tail.
  • Not starting the ogive at a cumulative frequency of zero.

Exam tips

  • Use your calculator's statistics mode for the mean and standard deviation, but write the values down clearly.
  • When interpreting standard deviation, say how many values lie within one standard deviation of the mean.
  • Start an ogive at the lower boundary of the first class with a cumulative frequency of 0.

Frequently asked questions

What does standard deviation tell you?

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

Do I divide by n or n − 1?

CAPS uses the population standard deviation, which divides by n. On a Casio calculator this is σx, not sx.

Is regression in Grade 11?

No. Scatter plots, the least squares regression line and the correlation coefficient are Grade 12 work.

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