Grade 10 Statistics

Grade 10 statistics: mean, median, mode, range, quartiles, interquartile range, five-number summary and box-and-whisker plots, with worked examples.

Grade 10 statistics is about 15 marks of Paper 2. You summarise data with measures of central tendency (mean, median and mode) and measures of dispersion (range, quartiles, interquartile range and percentiles), draw the five-number summary as a box-and-whisker plot, and work with grouped data using the modal class and an estimated mean.

The skill examiners look for is interpretation: saying what the numbers tell you about the data, comparing two data sets, and explaining which measure of centre is most suitable. Grade 11 adds standard deviation, histograms and ogives.

Key concepts

  • Mean, median and mode of ungrouped data
  • Range, quartiles (Q1, Q2, Q3) and interquartile range IQR = Q3 − Q1
  • Five-number summary and box-and-whisker plots
  • Grouped data: modal class, class containing the median and estimated mean
  • Choosing the best measure of central tendency

Worked examples

Find the interquartile range of 3; 5; 7; 8; 9; 11; 13; 15.

The median is (8 + 9)/2 = 8.5. Q1 is the median of 3; 5; 7; 8 = 6 and Q3 is the median of 9; 11; 13; 15 = 12. IQR = 12 − 6 = 6.

The mean of four numbers is 12. A fifth number, 22, is added. Find the new mean.

The four numbers total 4 × 12 = 48. New mean = (48 + 22) ÷ 5 = 14.

Write down the five-number summary of 2; 4; 4; 6; 8; 9; 10.

Minimum 2, Q1 = 4, median = 6, Q3 = 9, maximum 10.

Estimate the mean: 0 ≤ x < 10 has frequency 4 and 10 ≤ x < 20 has frequency 6.

Use the class midpoints, 5 and 15: (5 × 4 + 15 × 6) ÷ (4 + 6) = (20 + 90) ÷ 10 = 11. It is an estimate because we don't know the exact values in each class.

Common mistakes

  • Finding the median without sorting the data first.
  • Including the median in the halves when finding quartiles of an odd-sized set (your textbook's convention may differ, so be consistent).
  • Drawing a box-and-whisker plot without a scale.
  • Saying the mean is always the best measure, even with an outlier.

Exam tips

  • Sort the data and count the values before you do anything else.
  • When comparing two data sets, comment on both the centre and the spread.
  • Use the median when the data has outliers or is skewed.

Frequently asked questions

Is standard deviation in Grade 10?

No. Variance and standard deviation are introduced in Grade 11. Grade 10 uses the range, quartiles and interquartile range to describe spread.

What does a box-and-whisker plot show?

The five-number summary: minimum, lower quartile, median, upper quartile and maximum. The length of the box is the interquartile range.

How do I estimate the mean of grouped data?

Multiply each class midpoint by its frequency, add these products and divide by the total frequency.

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