This free online statistics calculator will calculate the mean, median, mode, minimum, maximum, and range of a data set.
You can either enter the numbers in the data set one at a time, or you can copy and paste an existing data set (if separated by spaces, commas, line returns, or any combination thereof), or you can enter a number and its frequency (12x4, 8x6, 9x4) to get the weighted average from grouped data within a data set.
Plus, unlike other online statistics calculators, this calculator will generate and display a distribution table in the results so you can see how many times each of the numbers is repeated within the data set.
To show how to calculate mean, median, mode, and range, I will use the following data set:
The mean is the average of all numbers in a data set. To calculate the mean of set of numbers, you add all of the numbers together and then divide that sum by the number of elements within the set.
Data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13, 23 
Data set contains 13 numbers 
Mean = (36 + 3 + 8 + 12 + 15 + 18 + 22 + 34 + 8 + 25 + 17 + 13 + 23) ÷ 13 
Mean = 234 ÷ 13 
Mean = 18 
The median is the middle number in a data set after sorting the data set from smallest to largest. To calculate the median of a data set, you count the number of elements and then sort the elements from smallest to largest. Next, for an odd number of elements, you add 1 to the number of elements and then divide by 2 to get position of the middle number. From our example data set, the median is the 7th number in the sorted list, which is the number 17.
Odd numbered data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13, 23  
Number of elements in set is 13  
Middle Position = ((count + 1) ÷ 2)  
Middle Position = ((13 + 1) ÷ 2)  
Middle Position = (14 ÷ 2)  
Middle Position = 7  
Count  1  2  3  4  5  6  7  8  9  10  11  12  13 
Data Set  3  8  8  12  13  15  17  18  22  23  25  34  36 
Median = 17 (7th number in sorted data set) 
Note that for an even number of elements, you find the average of the two middle numbers. The first middle position would be equal to number of elements divided by 2 less 1. The second middle position would be the first middle position plus 1. You then add the two middle numbers together and divide by 2 to find the average. From our revised example data set, this gives you a medium of 16  which is the average of the 6th and 7th elements (15 and 17).
Even numbered data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13  
Number of elements in set is 12  
1st Middle Position = (count ÷ 2)  1  
1st Middle Position = (12 ÷ 2)  1 = 6  
1st Middle Number = 15  
2nd Middle Position = 1st Middle Position + 1  
2nd Middle Position = 6 + 1 = 7  
2nd Middle Number = 17  
Average of Middle Numbers = (15 + 17) ÷ 2 = 16  
Count  1  2  3  4  5  6  7  8  9  10  11  12 
Data Set  3  8  8  12  13  15  17  18  22  25  34  36 
Median = 16 (average of 15 and 17) 
The mode is the number in a data set that is repeated the most often within the set. To find the mode, you simply count the number of times each unique number appears within the data set. The number that appears most often is the mode. In our example data set, the number that appears the most often is 8, therefore the mode of the data set is 8.
Example data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13, 23  
Sorted Data Set  3  8  8  12  13  15  17  18  22  23  25  34  36 
Mode = 8 (8 appears the most often) 
Note that a data set can have more than 1 mode. For example, if the above data set included another 3, then the set would have two modes: 3 and 8. A data set having two modes is referred to as a bimodal set, whereas a data set having more than two modes is referred to as a multimodal set.
The range is the difference between the largest number within the set and the smallest number in the set. To find the range, you sort the range from smallest to largest to determine the minimum and maximum values. You then subtract the minimum value from the maximum value to find the range. In our example set the minimum is 3 and the maximum is 36, which would result in a range of 33 (36  3).
Example data set: 36, 3, 8, 12, 15, 18, 22, 34, 8, 25, 17, 13, 23  
Sorted Data Set  3  8  8  12  13  15  17  18  22  23  25  34  36 
Range = 33 (difference between maximum of 36 and minimum of 3) 
With that, let's use the Statistical Average Calculator to calculate the mean, median, mode, and range for a set of data.

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