The word “average” is used to describe a statistical quantity that is a measure of the central tendency of a set of numbers. It is a way to summarize a large amount of data in a single value, and is often used to compare different sets of data or to track changes over time.
There are several different types of averages, each with its own unique properties and uses. Here are some definitions of common types of averages:
- Mean: The mean is the arithmetic average of a set of numbers. It is calculated by adding all of the numbers in the set together and then dividing by the total number of numbers in the set.
- Median: The median is the middle number in a set of numbers that are ordered from smallest to largest. If there is an odd number of numbers in the set, the median is the number that is exactly in the middle. If there is an even number of numbers in the set, the median is the mean of the two middle numbers.
- Mode: The mode is the number that appears most frequently in a set of numbers. If all of the numbers in the set are unique, then the set has no mode.
- Range: The range is the difference between the largest and smallest numbers in a set. It is a measure of how spread out the numbers in the set are.
Here are five examples of how averages can be used:
- A teacher wants to know the average test score for her class on a recent exam. She adds up the scores of all of her students and divides the total by the number of students to get an average score of 80.
- A company wants to know the average salary of its employees. It adds up the salaries of all of its employees and divides the total by the number of employees to get an average salary of $50,000.
- A researcher wants to know the average height of adult males in a certain population. He measures the height of a large sample of males and calculates the mean height to be 5 feet, 10 inches.
- A weather station wants to track the average temperature in a certain location over the course of a year. It records the daily high and low temperatures and calculates the mean temperature for each day.
- An investor wants to know the average return on investment for a certain stock over the past 10 years. She calculates the mean annual return by adding up the returns for each year and dividing by the number of years.
Now, here is a quiz to test your understanding of averages:
- Which of the following is NOT a type of average? a) Mean b) Median c) Mode d) Range
- The mean of a set of numbers is always: a) Larger than the median b) Smaller than the median c) The same as the median d) None of the above
- The mode of a set of numbers is always: a) Larger than the mean b) Smaller than the mean c) The same as the mean d) None of the above
- The range of a set of numbers is always: a) Larger than the mean b) Smaller than the mean c) The same as the mean d) None of the above
- The median of a set of numbers can be affected by: a) The mean of the set b) The mode of the set c) The range of the set d) All of the above
