Unit 9 statistics Lesson 4 Measures of Center
Key concept: Measures of center, or central tendency, are statistics that describe the central or average value of a dataset. The most common measures of center are the mean, median, and mode.
Mean:
- The mean is calculated by adding up all the values in a dataset and then dividing by the total number of values.
- It is also known as the average.
- The mean can be influenced by outliers in the data.
Median:
- The median is the middle value when the data is arranged in numerical order.
- If there is an even number of data points, the median is the average of the two middle values.
- The median is resistant to outliers because it is not influenced by extreme values.
Mode:
- The mode is the value that occurs most frequently in a dataset.
- A dataset can have no mode (no value occurs more than once), one mode, or multiple modes.
- The mode is especially useful for categorical data.
Example:
Let's consider the following dataset: 2, 4, 5, 6, 8, 10, 12, 12, 15.
Mean = (2 + 4 + 5 + 6 + 8 + 10 + 12 + 12 + 15) / 9 = 7.89
Median = 8
Mode = 12
In this example, the mean is 7.89, the median is 8, and the mode is 12. Each measure of center provides different information about the dataset, and it is important to consider all three when analyzing data.