Finding Patterns in Data

Learning objectives

• Calculate mean, median, mode and range for a real dataset.
• Construct a scatter plot from two variables and describe any apparent correlation.
• Explain the difference between correlation and causation with examples.
• Identify potential confounding variables that might explain an observed correlation.

Background

Descriptive statistics summarise a dataset with a small number of meaningful numbers. The mean (average) gives the central tendency; the range (maximum minus minimum) gives the spread; the standard deviation measures how much individual values deviate from the mean on average. Together these numbers give a compact description of what a dataset contains.

A correlation is a statistical relationship between two variables — when one tends to be higher when the other is higher (positive correlation) or lower (negative correlation). For example, air temperature and humidity in Nepal tend to be positively correlated during monsoon season (both are high) but negatively correlated in winter (warm sunny days have low humidity). Correlations can be visualised as scatter plots and quantified with a correlation coefficient (r) from -1 to +1.

The critical caution: correlation does not imply causation. Two variables can be correlated because one causes the other, because both are caused by a third variable, or simply by chance. Ice cream sales and drowning rates are correlated — not because ice cream causes drowning, but because both increase in summer (a confounding variable). In environmental science, claiming causation from correlation alone has led to expensive policy mistakes.

Procedure

1. Collect data: record air temperature and humidity for 10 time points from the history chart. Note the timestamps.
2. Calculate: mean temperature, mean humidity, range for each. Show your working.
3. Plot a scatter diagram: x-axis = temperature, y-axis = humidity. Each data point is one reading.
4. Describe the correlation you see in the scatter plot: positive, negative, none, or non-linear?
5. Calculate the ratio of each temperature reading to the corresponding humidity reading. Does this ratio stay constant, or does it vary?
6. Hypothesis test: "Higher temperature causes higher humidity at this station." Is this supported by your data? What alternative explanation might explain the same pattern?

Discussion

1. You find that soil moisture and air humidity are strongly correlated in your data. Does this prove that humid air causes wetter soil? What else might explain the correlation?
2. A newspaper headline reads: "Scientists find link between humidity and crop yield." What would you need to know before believing that humidity causes yield changes?
3. What additional data would you need to collect to test whether temperature causes humidity to change at this station, rather than both being caused by a third factor?

Worksheet

Vocabulary

Correlation

A statistical relationship between two variables — when one tends to increase or decrease as the other does.

Causation

A relationship where one thing directly produces or influences another.

Scatter Plot

A graph where each point represents a pair of values from two variables, used to visualise correlations.

Standard Deviation

A measure of how spread out values in a dataset are from the mean — larger means more variability.

Extension

Use spreadsheet software to calculate the Pearson correlation coefficient (r) for your temperature and humidity data. Interpret the result: what does an r of +0.7 or −0.4 tell you? Find the formula for r and understand each step.