Reading data: charts, mean, median, mode and range
Before you start: Add a list of numbers, divide a total and compare values.
Read the chart before calculating
Check the title, category labels, units and tick spacing. A bar at 4 may mean four items or four thousand items, depending on the scale. A frequency tells how many observations have a value. If one bar records three players with 10 points each, their combined contribution is 3 × 10 = 30 points, not 10.
Worked example: four summaries of one list
Use the scores 2, 4, 4, 6, 9. Their total is 25 and there are five observations, so the mean is 25 ÷ 5 = 5. Imagine redistributing all 25 points equally: each observation would receive 5. This is why the mean uses every value.
The list is already sorted. Its middle value, in position 3, is 4, so the median is 4. The most frequent value is also 4, appearing twice, so the mode is 4. Finally the range is 9 − 2 = 7, a measure of spread, not a centre.
Even-sized lists and tied modes
For 2, 4, 6, 10, the two middle values are 4 and 6. Their mean, (4 + 6)/2 = 5, is the median; it need not appear in the list. A list can have multiple equally frequent modes. If every value occurs once, it is commonly described as having no mode.
How an outlier affects the summaries
Replace 9 with 99 in the first list. The total becomes 115 and the mean becomes 23, while the median and mode remain 4. The range becomes 97. The mean is still calculated correctly, but it may describe a typical observation poorly here. Choose a summary to answer a question rather than assuming one is always best. A chart or the original list helps reveal what a single summary hides.
Try it yourself
For the sorted list 3, 3, 5, 9, find the mean, median, mode and range.
Show answer and explanation
The total is 20, so the mean is 5. The middle values are 3 and 5, so the median is 4. The mode is 3 and the range is 6.
Use the activity to check your understanding
Change one value in the visualizer. Predict which summaries will change before reading the new results.