Level 3 Mathematical Studies (Core Maths) AQA

Measures of Central Tendency

Measures of Central Tendency

Mean

• The mean is calculated by adding up all the numbers in a dataset and dividing by the count of numbers in the dataset.
• It gives the average value of the dataset.
• One disadvantage is that the mean can be heavily affected by outliers or extremes values.

Median

• The median is the middle value in a dataset when arranged in ascending order.
• If there is an even number of values, the median is the mean of the two middle numbers.
• The advantage of using median is it isn't affected by outliers or extreme numbers.

Mode

• The mode is the value that occurs most frequently in a dataset.
• A dataset may have one mode (unimodal), two modes (bimodal), more than two modes (multimodal), or no modes (no repeated values).

Key Differences

• The three measures can provide different insights: the mean considers all values, the median represents the middle point, and the mode identifies the most common values.
• Outliers may affect the mean significantly, can change median slightly but never affect the mode.
• The mean can be less representative if the dataset is skewed, while the median and mode are more resilient to skewed data.

Practice Problem

• For instance, in the set {3, 5, 6, 6, 9}:
  • The mean is (3+5+6+6+9)/5 = 5.8.
  • The median is 6 (the middle value).
  • The mode is 6 (the most frequently occurring value).