Types of data (quantitative and qualitative; primary and secondary) and descriptive statistics: measures of central tendency (mean, median, mode), the range, percentages and ratios, and ways of presenting data (tables, bar charts and scatter graphs).

What this dot point is asking

OCR wants you to know the types of data (quantitative and qualitative; primary and secondary) and the descriptive statistics you must be able to calculate: the measures of central tendency (mean, median, mode), the range, percentages and ratios, and how to present data (tables, bar charts and scatter graphs). This is the topic that carries the maths marks.

Types of data

• Quantitative data is easy to analyse and compare statistically but can lack depth.
• Qualitative data is rich and detailed but harder to analyse objectively.
• Primary data is collected first-hand by the researcher for the study; secondary data comes from existing sources (such as official statistics or other studies).

Measures of central tendency

These summarise the "typical" value in a data set:

• Mean ($\bar{x}$): add up all the values and divide by how many there are: $\bar{x} = \dfrac{\sum x}{n}$. It uses every value but is distorted by extreme values (anomalies).
• Median: the middle value when the data are put in order. If there are two middle values, take their mean. It is not affected by extremes but ignores the actual values.
• Mode: the most frequent value. It is the only one that works for categories, but a data set can have no mode or several.

The range and other maths

The range measures spread (dispersion): $\text{range} = \text{largest value} - \text{smallest value}$. A larger range means more spread-out data. You must also be confident with:

• Percentages: a proportion out of 100. To turn a fraction into a percentage, multiply by 100: for example, 18 out of 24 is $\dfrac{18}{24} \times 100 = 75\%$.
• Ratios: comparing quantities, such as 12 boys to 18 girls written as $12:18$, which simplifies to $2:3$.

Presenting data

• Tables organise raw data and summary statistics clearly.
• Bar charts show data for separate categories (the bars have gaps), for example mean recall in two conditions.
• Scatter graphs plot two variables against each other to show a correlation (see non-experimental methods).

Evaluating the statistics

Descriptive statistics matter because they make raw data understandable and comparable. The mean is the most informative average (it uses every value) but is distorted by anomalies; the median resists anomalies but ignores the actual values; the mode suits categorical data but can be unstable. The range is a quick measure of spread but only uses the two extreme values, so it can be misleading if there is an outlier. Choosing the right statistic and graph for the data, and being aware of these limitations, is exactly what OCR rewards in the maths and "interpret a source" questions on Paper 2.

Try this

Q1. Calculate the mean of 4, 7, 7, 10, 12. Show your working. [2 marks]

• Cue. $\dfrac{4 + 7 + 7 + 10 + 12}{5} = \dfrac{40}{5} = 8$.

Q2. Which measure of central tendency is least affected by an extreme value? [1 mark]

• Cue. The median.

Q3. Express 15 out of 20 as a percentage. [1 mark]

• Cue. $\dfrac{15}{20} \times 100 = 75\%$.