Understanding Statistical Measures: Mean, Median, and Mode
Statistical analysis helps us understand data patterns and make informed decisions. Let's explore three fundamental measures of central tendency using detailed examples and clear explanations.
Definition: Mean is the arithmetic average found by adding all numbers and dividing by how many numbers there are. Median is the middle value when numbers are arranged in order. Mode is the value that appears most frequently in a dataset.
When working with the dataset 72, 73, 79, 84, 84, 84, 90, 90, 97, we can calculate each measure systematically. To find the mean, add all numbers (753) and divide by the count of numbers (9), giving us 83.67. This represents the average value in our dataset, providing a balanced measure of central tendency.
For finding the median, first arrange numbers in ascending order: 72, 73, 79, 84, 84, 84, 90, 90, 97. With 9 numbers, the middle (5th) position gives us 84. When dealing with an even number of values, take the average of the two middle numbers. The median of 84 indicates that half the values lie above and half below this point.
Example: Mode calculation
- Dataset: 72, 73, 79, 84, 84, 84, 90, 90, 97
- 84 appears three times
- 90 appears twice
- Other numbers appear once
- Therefore, the mode is 84