Statistics 1

Section 1What statistics is

Statistics is the collection, organisation, presentation, and interpretation of data. Data are facts or values gathered to answer a question. In plain words, statistics helps you move from 'I think' to 'the data suggest'.

Section 2Collecting data

Data can be collected by surveys, observations, experiments, interviews, or from existing records. A sample is a smaller group chosen from a population. Watch out: a biased sample gives misleading results, even if the calculations are correct.

Section 3Types of data

Qualitative data describe categories, such as favourite sport or parish. Quantitative data are numerical, such as height, age, or test score. Quantitative data may be discrete, like number of siblings, or continuous, like mass or time.

Section 4Scales of measurement

Nominal data are names or categories with no natural order. Ordinal data have an order, like first, second, third. Interval data have equal gaps but no true zero, while ratio data have equal gaps and a true zero, such as distance or mass.

Section 5Tables and charts

A frequency table records how often each value or category appears. Bar charts compare categories, pie charts show parts of a whole, line graphs show change over time, and histograms are used for grouped continuous data. Easy to mix up - bar charts have gaps; histograms usually do not.

Section 6Averages

The mean is found by adding all values and dividing by the number of values. The median is the middle value after ordering the data. The mode is the most frequent value. The thing to remember is that the best average depends on the data and the question.

Section 7Range and interpretation

Range measures spread by subtracting the smallest value from the largest value. Averages tell you a typical value, but range tells you how spread out the data are. For example, two classes can have the same mean quiz score but very different ranges.