Descriptive Statistics

1. Categorical Data (Sample Size & Proportions)

When analysing categorical data, we look at the sample size (the total number of observations) and proportions (the number of specific responses divided by the sample size).

Proportions can be written as decimals, fractions, or percentages. They are incredibly useful for fairly comparing groups of different sizes.

2. Numerical Data (Location & Spread)

To summarise numerical data, you must calculate one measure of location (an average) and one measure of dispersion (how spread out or consistent the data is). These measures must always be paired correctly based on the distribution of the data:

• Normally Distributed Data: Use the mean (location) and the standard deviation (spread).
• Skewed Data (Positive or Negative): Use the median (location) and the interquartile range / IQR (spread). This is because extreme outliers in the 'tail' of skewed data will drastically distort the mean, but the median remains unaffected.

3. Making Valid Comparisons

A massive part of the Higher Applications course is comparing two datasets. To gain full marks, you must always write two separate sentences in the context of the question:

• Sentence 1 (Location): Compare the averages using the word "average", state which is higher/lower, and explicitly state the numbers.
  (e.g., "On average, Group A was faster because its median (12s) is lower than Group B's (15s).")
• Sentence 2 (Spread): Compare the spread using the word "consistent" or "varied", and explicitly state the numbers.
  (e.g., "Group A's times were more consistent because its IQR (2s) is smaller than Group B's (5s).")

4. R Studio Commands

• mean(X) / sd(X) - calculates the mean and standard deviation.
• median(X) / IQR(X) - calculates the median and interquartile range.
• summary(X) - provides the 5-figure summary (min, Q1, median, mean, Q3, max).
• prop.table(table(X)) - calculates the proportions of a categorical variable.