Charts & averages

Data handling starts with organizing data clearly, choosing suitable charts, and summarizing a dataset with averages.

Frequency tables

A frequency table records each value (or class interval) and how often it appears. For grouped data, use class midpoints for estimation.

Common charts

• Bar chart: categorical comparisons.
• Histogram: continuous grouped data (touching bars).
• Line graph: change over time.
• Pie chart: part-to-whole proportions.
• Box plot: spread via quartiles and median.

Mean, median, and mode

\[ \text{Mean}=\frac{\text{sum of values}}{\text{number of values}}. \]

Median is middle value when ordered. Mode is most frequent value.

Mean from frequency table

\[ \bar{x}=\frac{\sum fx}{\sum f}. \]

where \(x\) is value (or midpoint), \(f\) is frequency.

Choosing an average

• Use mean when data has no extreme outliers.
• Use median when distribution is skewed.
• Use mode for most common category/value.

Exam strategy

• Label axes and units clearly on charts.
• Check scale intervals before reading values.
• Order data before finding median and quartiles.
• State if an answer is estimated from grouped data.

Checkpoints