Mean-Median-Mode Calculator
Solution:
Mean:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is $$ \mu = \frac{{\sum}x}{N} $$ The formula for the mean of a sample is $$ \bar{x} = \frac{{\sum}x}{n} $$ Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is: $$ \frac{2264}{12} = 188.6667$$
Median:
The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:
$$ 108, 125, 135, 136, 142, 189, 199, 213, 241, 241, 245, 290 $$
Since there is an even number of data values in this data set, there are two middle numbers. With 12 data values, the middle numbers are the data values at positions 6 and 7. These are 189 and 199. The median is the average of these numbers. We have $$ {\frac{ 189 + 199 }{2}} $$ Therefore, the median is $$ 194 $$
Mode:
The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, the mode(s) is/are