Numerical and statistical skills: calculating and interpreting measures of central tendency (mean, median, mode) and spread (range, interquartile range), percentages and percentage change, ratios and proportions, and reading data from tables and graphs.

What this dot point is asking

This covers the numerical and statistical skills assessed across every component of Eduqas GCSE Geography A (C111), and tested most directly in Component 3, Applied Fieldwork Enquiry. At least 10 percent of the marks across the GCSE are for quantitative skills. Eduqas expects you to calculate and interpret measures of central tendency (mean, median, mode) and spread (range, interquartile range), percentages and percentage change, ratios and proportions, and to read data from tables and graphs.

Measures of central tendency

These three "averages" summarise a data set, and Eduqas wants you to know when each is useful.

For example, for the data $2, 3, 3, 4, 8$: the mean is $\frac{2+3+3+4+8}{5} = \frac{20}{5} = 4$; the median (middle of five) is $3$; the mode is $3$.

Measures of spread

Spread shows how varied the data are.

• The range is the largest value minus the smallest: simple, but distorted by a single extreme value.
• The interquartile range (IQR) is the spread of the middle half of the data. Order the data, find the lower quartile ($Q_1$, the value a quarter of the way through) and the upper quartile ($Q_3$, three quarters of the way through), then $\text{IQR} = Q_3 - Q_1$. Because it ignores the extreme quarter at each end, the IQR is not distorted by outliers.

Percentages and percentage change

Percentages let you compare data fairly.

• A percentage is a part out of 100: $\dfrac{\text{part}}{\text{whole}} \times 100$.
• Percentage change measures how much something has grown or shrunk:
  
  $$\text{percentage change} = \frac{\text{new value} - \text{original value}}{\text{original value}} \times 100$$
• The crucial rule is to divide by the original value, not the new one. A positive answer is an increase; a negative answer is a decrease.

Ratios and proportions

A ratio compares two quantities, written as $a : b$. For example, if a survey finds 30 cars and 10 lorries, the ratio of cars to lorries is $30 : 10$, which simplifies to $3 : 1$. A proportion expresses one part of the whole, often as a fraction or percentage (10 lorries out of 40 vehicles is $\frac{10}{40} = 25\%$).

Reading data from tables and graphs

Many marks come simply from reading values accurately: take figures off a table, read a point off a line or bar graph, find a value on a scatter graph, or describe a trend (rising, falling, steady) and spot anomalies (values that do not fit the pattern). Always quote figures and units to support a description.

Try this

Q1. For the data 4, 6, 6, 7, 12, calculate the mean, median and mode. [3 marks]

• Cue. Mean = $\frac{4+6+6+7+12}{5} = 7$; median (middle of five) = 6; mode = 6.

Q2. A village population fell from 800 to 600. Calculate the percentage decrease. [2 marks]

• Cue. $\frac{800-600}{800} \times 100 = 25\%$ decrease (divide the change by the original).