Different Measures of Data

This section explains the numerical and statistical skills needed to GCSE fieldwork studies. In geography, understanding and using numerical data effectively is essential for carrying out fieldwork, drawing conclusions, and identifying trends or patterns. Numerical skills help geographers to calculate, analyse, and interpret data, allowing them to make predictions and support their conclusions with evidence. Here’s a guide to some key measures of data and how they are used in geographical analysis.

Different Measures of Data

Geographical data is collected in a variety of ways, and knowing how to process and understand this data is crucial for interpreting trends. Below are the main measures of data used in geography:

Median

The median is the middle value in a set of numbers when they are arranged in order. If there is an odd number of values, the median is the exact middle number. If there is an even number of values, the median is the average of the two middle values.

Example:

If you have the following data set showing the temperatures of a location over five days: 12°C, 15°C, 14°C, 18°C, and 10°C, first order the data: 10°C, 12°C, 14°C, 15°C, 18°C. The median temperature is 14°C because it is in the middle.

Mean (Average)

The mean (or average) is calculated by adding up all the values in a data set and then dividing the total by the number of values. It is one of the most common ways to summarise data.

Example:

Consider the following river flow measurements in litres per second: 5, 8, 7, 10, and 6.
To calculate the mean:

• Add all the numbers: 5 + 8 + 7 + 10 + 6 = 36.
• Divide by the number of values (5): 36 ÷ 5 = 7.2. So, the mean flow rate is 7.2 litres per second.

Range

The range is the difference between the largest and smallest values in a data set. It provides a quick sense of how spread out the data is.

Example:

If the highest temperature recorded in a city in a week was 22°C and the lowest was 16°C, the range would be:

• Range = 22°C - 16°C = 6°C.

Quartiles

Quartiles are values that divide a data set into four equal parts. The first quartile (Q1) represents the value below which 25% of the data fall, the second quartile (Q2) is the median, and the third quartile (Q3) represents the value below which 75% of the data fall.

Interquartile Range (IQR)

The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1). It shows the range within which the middle 50% of the data fall and is useful for understanding the spread of the central data points, excluding outliers.

Example:

If Q1 = 7 and Q3 = 15, then:

• Interquartile Range = 15 - 7 = 8.

For more information on calculating averages click here. 

Calculating Percentage Change

Geographers often calculate the percentage change (increase or decrease) in data over time or between different locations to identify trends.

Percentage Increase

To calculate percentage increase, find the difference between the new value and the original value, then divide the increase by the original value and multiply by 100.

Formula:
Percentage increase = increase/ original number × 100

Example:

If the number of tourists visiting a coastal town increases from 500 to 600:

• The increase = 600 - 500 = 100.
• Percentage increase = 100/500 × 100=20%

So, the percentage increase in tourists is 20%.

Percentage Decrease

To calculate percentage decrease, subtract the new value from the original value, divide by the original number, and multiply by 100.

Formula:
Percentage decrease = decrease/original number × 100

Example:

If the number of seabirds in a coastal area decreases from 200 to 150:

• The decrease = 200 - 150 = 50.
• Percentage decrease = 50/200×100=25%

So, the percentage decrease in seabird numbers is 25%.

Percentiles

Percentiles divide data into 100 equal parts, allowing for more granular analysis of data distributions. While quartiles divide data into four parts, percentiles provide 100 divisions.

For example, if a student’s exam score is in the 90th percentile, it means that the student’s score is higher than 90% of other students’ scores.

Example:

In a study of the heights of 100 people, the 90th percentile would represent the height below which 90% of people fall. If a person is in the 90th percentile for height, they are taller than 90% of the population in the study.

For more information on calculating percentages click here. 

Identifying Relationships in Data

Recognising patterns and relationships in data is a crucial part of geographical analysis. Geographers use different techniques to explore and interpret data, and the relationships between variables can help predict future trends.

Scatter Graphs

Scatter graphs show the relationship between two sets of data, plotting each pair of values as points on a graph. The relationship between the variables can be analysed by examining the pattern of points.

• Positive Correlation: As one variable increases, the other also increases. The points on a scatter graph will move upwards from the bottom left to the top right.
• Negative Correlation: As one variable increases, the other decreases. The points will move downwards from the top left to the bottom right.
• No Correlation: There is no clear relationship between the variables, and the points will be scattered randomly across the graph.

Example:

If you are studying the relationship between the number of tourist facilities and the number of visitors to a location, you may find a positive correlation, meaning that as the number of facilities increases, the number of visitors also increases.

Line of Best Fit

A line of best fit is a straight line drawn through a scatter graph that represents the trend in the data. This line helps to visualise the relationship between the two variables.

• A strong correlation occurs when most points lie close to the line.
• A weak correlation occurs when the points are scattered further from the line.

Interpolation and Extrapolation

• Interpolation involves estimating a value within the range of data already collected. For instance, if you know the temperature for 10am and 2pm, you could use interpolation to estimate the temperature at 12pm.
• Extrapolation involves estimating a value outside the range of the data. This method is more uncertain because it predicts trends beyond the known data.

Example:

If a scatter graph shows the relationship between temperature and time of day, interpolation might be used to predict the temperature at 1pm, even if no data was collected at that specific time. Extrapolation could be used to predict the temperature at 6pm based on existing trends.

For more information on representing data click here. 

Mode and Modal Class

Mode

The mode is the most frequent value in a data set. It is useful when identifying the most common occurrence.

Example:

In a study of the number of shops in different areas, if most areas have 10 shops, then 10 is the mode.

Modal Class

The modal class is the range or group that appears most frequently in a frequency distribution. For example, in a study of ages, if most people fall within the age range of 20-30, this is the modal class.

By mastering these key numerical and statistical skills, geographers can analyse data more effectively, draw conclusions from fieldwork, and make predictions based on trends. Understanding how to apply and interpret these measures is essential for GCSE Geography and for real-world geographical analysis.