Averages and range
- Mean: add up the values and divide by how many there are. Median: the middle value when they are in order (with an even number of values, the mean of the middle two). Mode: the most common value. Range: highest − lowest.
- For 3, 5, 5, 8, 9: the mean is 30 ÷ 5 = 6, the median is 5, the mode is 5 and the range is 6.
- The mean uses every value but is affected by extreme values (outliers). The median isn't affected much by outliers. The mode can be used for data that isn't numbers, such as favourite colours.
Frequency tables
- Mean from a frequency table = total of (value × frequency) ÷ total frequency.
- For scores 1, 2 and 3 with frequencies 2, 3 and 5: the total is 2 + 6 + 15 = 23, and the mean is 23 ÷ 10 = 2.3.
Charts and graphs
- Bar charts and pictograms compare categories. Line graphs show how something changes over time.
- Pie charts: the angle for each sector = frequency ÷ total × 360°.
- Scatter graphs show whether two things are related: positive correlation (both increase), negative correlation (one increases as the other decreases) or no correlation. A line of best fit can be used to make estimates.
Comparing data
- Compare an average (such as the mean or median) and the range.
- A smaller range means the data is more consistent.
Key terms
- Mean
- The total of the values divided by the number of values.
- Median
- The middle value when the data is in order.
- Mode
- The value that appears most often.
- Range
- The difference between the highest and lowest values.
- Outlier
- A value that is much bigger or smaller than the rest.
- Frequency
- How many times something occurs.
- Pie chart
- A circle divided into sectors that show proportions.
- Scatter graph
- A graph of points that shows whether two sets of data are related.
- Correlation
- A relationship between two sets of data.
- Line of best fit
- A straight line drawn through the middle of the points on a scatter graph.