Cambridge IGCSE Mathematics Notes 9: Statistics

Cambridge IGCSE Mathematics 0580 Topic 10 covers data classification, interpretation, averages, spread, standard charts and scatter diagrams. Extended adds grouped-data estimates, modal class, graphic-display-calculator linear regression and cumulative frequency diagrams. Core grouped-data calculator mean is still listed, although hand calculation of grouped estimates sits in Extended content.

1. Classify and tabulate data

Categorical data record labels or groups; numerical data record quantities. Discrete data take separated countable values, while continuous data can take any value in an interval and arise from measurement.

Tally and frequency tables organise one variable. Two-way tables cross-classify two variables and must include consistent row, column and grand totals. A total mismatch signals a missing or duplicated observation.

Class boundaries matter for continuous grouped data. Adjacent intervals should cover the data without gaps or overlaps.

2. Interpret evidence cautiously

Read title, axes, units, scale, source and sample before making a claim. A graph shows the collected data, not necessarily a wider population or a causal relationship. Restrictions may arise from small samples, biased selection, missing groups, unequal measurement methods or extrapolation.

A comparison should address both typical value and spread. “Group A is better” is vague; state which measure is higher or lower, how variable each group is and whether the distributions overlap.

3. Mean, median, mode and quartiles

The mean uses every value and equals total divided by frequency. The median is the middle ordered value, while the mode is most frequent. Quartiles divide ordered data into four parts. The range is maximum minus minimum and interquartile range is upper quartile minus lower quartile.

Mean is responsive to extreme values. Median and interquartile range are more resistant and often suit skewed data. Mode can summarise categorical data. Select measures from distribution and purpose rather than habit.

For a frequency table, multiply value by frequency before summing. A scientific calculator can find mean, median and quartiles for discrete data, but input frequencies correctly and interpret its output.

4. Extended grouped data

For grouped discrete or continuous data, exact individual values are unknown. Estimate the mean by representing every class with its midpoint, multiplying midpoint by frequency, summing and dividing by total frequency.

The modal class is the class with greatest frequency in the grouped distribution. It is an interval, not an exact mode. State that a midpoint mean is estimated because it assumes the class observations balance at their midpoint.