What is a Measure of Central Tendency?
A measure of central tendency is a single value that describes the center or typical value of a data set. The three main measures are mean, median, and mode.
What is the Mean?
The mean (or average) is the sum of all data values divided by the number of values.
\[
\text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} = \frac{\sum x_i}{n}
\]
What is the Range?
The range is the difference between the highest and lowest values in a data set. It measures how spread out the data is.
\[
\text{Range} = \text{Maximum value} - \text{Minimum value}
\]
Interpreting Data:
- The mean is useful when data is evenly distributed (no extreme outliers)
- A large range indicates data is spread out; a small range indicates data is clustered
- The mean can be affected by extremely high or low values (outliers)
Real-Life Applications:
- Mean: average test scores, average rainfall, average salary
- Range: temperature variation, price spread in a market