To find the mean, median, and mode of a data set, we need to follow a few simple steps for each measure of central tendency.
Mean
The mean is calculated by adding all the numbers in the data set and then dividing by the total number of values. For example, if our data set is [2, 3, 5, 7, 11], we would perform the following calculation:
- Add the numbers: 2 + 3 + 5 + 7 + 11 = 28
- Count the total values: There are 5 numbers in this data set.
- Divide the total by the number of values: 28 / 5 = 5.6
So, the mean of this data set is 5.6.
Median
The median is the middle number of a sorted data set. If there is an odd number of values, the median is the middle one. If there is an even number, it is the average of the two middle numbers. Using the same data set [2, 3, 5, 7, 11], we first sort it (though it’s already sorted here) and find the middle value:
- There are 5 numbers (which is odd), so the median is the third number: 5.
The median of this data set is 5.
Mode
The mode is the number that appears most frequently in the data set. If no number repeats, the data set is said to have no mode. Looking at our data set [2, 3, 5, 7, 11], each number appears only once:
- No number repeats, thus there is no mode in this data set.
In conclusion, for the data set [2, 3, 5, 7, 11]:
- Mean: 5.6
- Median: 5
- Mode: None