Finding the mean, median, and mode involves different calculations and considerations for a given data set. Here's how to determine each:
Mean
The mean, also known as the average, is calculated by summing all the values in a data set and then dividing by the total number of values.
-
Formula: Mean = (Sum of all values) / (Number of values)
-
Example: For the data set {2, 4, 6, 8, 10}, the mean is (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
Median
The median represents the middle value in a data set that is ordered from least to greatest.
-
Odd Number of Values: If the data set contains an odd number of values, the median is the middle value.
- Example: In the ordered data set {1, 3, 5, 7, 9}, the median is 5.
-
Even Number of Values: If the data set contains an even number of values, the median is the average of the two middle values.
- Example: In the ordered data set {2, 4, 6, 8}, the median is (4 + 6) / 2 = 5.
-
Ordering the data: You must first order the data from the least to the greatest value.
Mode
The mode is the value that appears most frequently in a data set.
-
Example: In the data set {2, 2, 3, 4, 4, 4, 5}, the mode is 4 because it appears three times, which is more than any other value.
-
No Mode: If all values appear with the same frequency, the data set has no mode. For example, the data set {1, 2, 3, 4, 5} has no mode.
-
Multiple Modes: A data set can have more than one mode if multiple values appear with the same highest frequency. For example, in the data set {1, 2, 2, 3, 3, 4}, both 2 and 3 are modes.
