What are the main measures of central tendency in statistics?

Measures of Central Tendency: Definition

Measures of central tendency are statistical values that represent the center or typical value of a dataset. The three main measures are:

• Mean: The arithmetic average of all data points.
• Median: The middle value when data are ordered.
• Mode: The most frequently occurring value in the dataset.

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Worked Example

Consider the dataset: $4, 7, 7, 10, 12$ ### 1. Mean The mean is calculated as: %%MATH_DISPLAY_0%% ### 2. Median Order the data (already ordered): $4, 7, 7, 10, 12$ Since there are $5$ values (odd number), the median is the third value: %%MATH_DISPLAY_1%% ### 3. Mode The value that appears most frequently is $7$ (it appears twice):

$$ \text{Mode} = 7 $$

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Takeaways

• The mean uses all data values and is sensitive to outliers.
• The median is robust to outliers and best for skewed distributions.
• The mode shows the most common value and is useful for categorical data.