Mathematical Studies (Core Maths)

Analysis of Data

# Measures of Central Tendency

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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).

- The