Averages Name_______________________

The RANGE is the difference between the least and greatest amounts.

The FREQUENCY is the number of times an amount is present.

The MAXIMUM is the greatest amount in a set of data.

The MINIMUM is the least amount in a set of data.

Example: data: 4, 6, 9, 6, 6, 2, 2, 1, 8
Range is (9 - 1) 8
Frequency of 1 is 1, of 2 is 2, of 4 is 1, of 6 is 3, of 8 is 1, of 9 is 1
Maximum is 9
Minimum is 1

The MEAN is a summary statistic that gives a general sense of a set of data. Also, it can be seen as the “middle” with the number for which the total of the differences from it to the data below it balances the total of the differences from it to the data above it. The mean is the value of each data point should all the data be redistributed equally. It is usually found by adding up all the data and dividing by the number of points totalled.
In common usage, the word “average” is used as a synonym for mean. However, in math there are other averages.
The mean as a set of data:
- increases if any piece of data increases
- decreases if any piece of data decreases
- increases if a piece of data below the existing mean is removed
- decreases if a piece of data above the existing mean is removed

The MEDIAN is another type of average which tells the middle number in a set of data. To find the median, rearrange the data from least to greatest and find the middle number.

The MODE is another type of average which tells the piece of data which appears most often.

Example: data: 5, 6, 9, 6, 6, 2, 2, 1, 8
Mean: 5 + 6 + 9 + 6 + 6 + 2 + 2 + 1 + 8 = 45 / 9 = 5
Median: 1, 2, 2, 5, 6, 6, 6, 8, 9 = 6
Mode: 1, 2, 2, 5, 6, 6, 6, 8, 9 = 6

Mean, median, and mode averages are used to find different solutions, e.g., A baseball player’s batting average is a mean. If the average price of a house in a particular subdivision is reported, however, it might more likely be a median or a mode. The mode is usually the average used to describe shoe sizes at a store.

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