Interpreting data

The essentials

Interpreting data means reading summaries, tables and charts to draw correct conclusions and make decisions. Good interpretation chooses the right measure, notices unusual values, and avoids claiming more than the data shows.

Key points

• Outlier: a value far away from most others. It can be a genuine extreme or an error in recording.
• The mean is affected strongly by outliers; the median is not. For salaries 12, 15, 11, 14 and 98 (thousand rupees), the mean is 30 but the median is 14, which better represents a typical salary.
• The mode suits categorical data, such as the most popular colour or the most common shoe size.
• Use the standard deviation or range to compare consistency: of two batsmen with the same average score, the one with the smaller standard deviation is more consistent.
• Charts help interpretation: line charts show trends over time; bar charts compare categories; histograms show the distribution of a variable; scatter plots show relationships between two variables.
• Correlation is not causation: two quantities rising together does not prove that one causes the other.
• Conclusions depend on the sample. A survey of only one class may not represent the whole school.
• Data should be checked for missing, duplicate or wrong entries before analysis.

Exam tips

• When a data set has an extreme value, prefer the median to describe the centre.
• When asked "which is more consistent", compare standard deviations, not means.

Common mistakes

• Using the mean to describe a typical income in data with a few very high incomes.
• Drawing conclusions about a whole population from a small or biased sample.