Review: data displays, mean, median, mode and range
Discover Mathematics P6: Term 1, Units 1–7, Review
GoalRevise statistical questions, histograms, box plots and the measures of centre and spread.
New words
mean · the total divided by the number of valuesmedian · the middle value of the ordered datamode · the most common valuerange · largest value minus smallest value
Explanation
A statistical question has answers that vary. For numerical data we use a dot plot (every value), a histogram (equal intervals, touching bars) or a box plot (five-number summary: minimum, Q1, median, Q3, maximum). The mean is the fair share or balance point (total ÷ number of values). The median is the middle of the ordered data, the mode is the most common value, and the range (largest minus smallest) measures the spread. An outlier pulls the mean the most, so the median often describes the typical value better.
★Remember
Mean = total ÷ count. Median = middle. Mode = most common. Range = largest − smallest. Outliers pull the mean.
Worked examples
Ten pupils took these minutes to solve a puzzle: 6, 8, 8, 9, 10, 10, 10, 12, 14, 23. Grouped in intervals of width 5, the histogram has 4 pupils in 5–9, 5 in 10–14, none in 15–19 and 1 in 20–24 (4 + 5 + 0 + 1 = 10). There is a gap at 15–19 and a tail to the right.
For the same data: the total is 110, so the mean is 110 ÷ 10 = 11. The median is (10 + 10) ÷ 2 = 10, the mode is 10 (three times) and the range is 23 − 6 = 17. The lower half 6, 8, 8, 9, 10 gives Q1 = 8, and the upper half 10, 10, 12, 14, 23 gives Q3 = 12. The long right whisker shows the outlier 23, which pulls the mean (11) above the median (10).
A missing value. Five friends have the mean 12 points, so the total is 12 × 5 = 60. Four of them have 10, 11, 13 and 15, which is 49 together. The fifth friend has 60 − 49 = 11 points.
Class activity
Data detective. Collect ten numbers from home life (for example the number of people at the table each day for ten days). Find the mean, median, mode and range, and draw a dot plot. Is there an outlier? Which number is most typical?
Practice
1
Is “How many pupils are in Primary 6 at your school?” a statistical question?
No. It has one answer.
2
Sort 14, 22, 9, 31, 18, 25, 12, 27, 6, 19 into the intervals 0–9, 10–19, 20–29, 30–39.
