Statistics for Matric Maths

Five-number summary, standard deviation, ogives, scatter plots and regression for NSC Paper 2. CAPS-aligned with AI step-by-step help.

Statistics in Paper 2 covers measures of central tendency and dispersion, five-number summaries, box-and-whisker plots, ogives, scatter plots, regression and the correlation coefficient. Statistics is usually the first question in Paper 2, which makes it a good place to secure marks early. You are given a data set or a frequency table and asked to calculate, represent and interpret. Interpretation answers must refer to the data in the question: say what the spread, skewness or correlation means for the learners, sales or measurements described, rather than only naming the statistic.

Key concepts

  • Mean, median, mode, range, IQR
  • Standard deviation (calculator)
  • Five-number summary and box plots
  • Ogives (cumulative frequency curves)
  • Least squares regression line and correlation coefficient r
  • Skewness from a box plot: symmetric, positively or negatively skewed
  • Estimated mean of grouped data using class midpoints
  • Outliers and their effect on the mean and standard deviation
  • Predicting with the regression line, and its limits outside the data range

Worked examples

Interpret r = 0.92 for a scatter plot.

Strong positive linear correlation — as x increases, y tends to increase, and the points lie close to a straight line.

Find the five-number summary of 3, 5, 7, 8, 9, 11, 12, 15.

Minimum 3 and maximum 15. Median = (8 + 9)/2 = 8.5. Q1 is the median of 3, 5, 7, 8, so Q1 = 6. Q3 is the median of 9, 11, 12, 15, so Q3 = 11.5. Summary: 3; 6; 8.5; 11.5; 15.

The mean of five numbers is 12. A sixth number is added and the mean becomes 13. Find the sixth number.

The original total is 5 × 12 = 60 and the new total is 6 × 13 = 78. The sixth number is 78 − 60 = 18.

Estimate the mean: 0 ≤ x < 10 (f = 4), 10 ≤ x < 20 (f = 6), 20 ≤ x < 30 (f = 10).

Use the midpoints 5, 15 and 25: (4 × 5 + 6 × 15 + 10 × 25) / 20 = (20 + 90 + 250) / 20 = 18.

Common mistakes

  • Reading the median off the x-axis instead of the y-axis on an ogive.
  • Confusing 'correlation' with 'causation' in interpretation questions.
  • Plotting an ogive at class midpoints instead of upper class boundaries.
  • Finding the median and quartiles before arranging the data in order.
  • Using the regression line far outside the data range without comment.

Exam tips

  • Always use the calculator's stats mode for standard deviation — don't try by hand.
  • Record the calculator's a, b and r values to at least two decimal places before rounding the final answer.
  • To describe skewness, compare Q3 − Q2 with Q2 − Q1, or compare the mean with the median.

In past papers

  • NSC Nov 2024 Paper 2 Q1–Q2 — box plot and regression

Frequently asked questions

Do I need to calculate standard deviation by hand?

No — CAPS allows scientific calculators and you should always use stats mode.

What is the difference between the IQR and the standard deviation?

The interquartile range Q3 − Q1 measures the spread of the middle 50% of the data and is not affected by outliers. The standard deviation measures how far all the values lie from the mean, so outliers affect it.

How do I draw an ogive?

Plot cumulative frequency against the upper boundary of each class, start at the lower boundary of the first class with a cumulative frequency of zero, and join the points with a smooth curve.

Do I calculate the regression line by hand?

No. Use your calculator's regression mode to find a and b in ŷ = a + bx, and the correlation coefficient r, then write the equation with the rounded values.

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