How to Use Median, Mean, Mode Range Calculator

Enter a data set separated by comma's : 1,2,3,44

Median, Mean, Mode Range Calculator




Median

The Median is essentially the middle value in a list of sorted numbers. It divides a data set, representing a value where 50% of the data set is lower then the value and the remaining 50% of the data set is higher.

When calculating the median of a fixed list of numbers, the order of the numbers is important. A list that is ordered generally starts with the lowest number and from there the list is done in ascending order although, it is possible to do the list in descending order and the result will be the same.

A quick way to find the middle is to count all the numbers in a data set, then add 1 and divide the by 2. This works for both uneven and even lists. If a even list has 9 numbers, we add our one which is 10, now divide by 2 which results in 5. the 5th number is our median. We have another data set were there is 12 numbers, we add 1 = 13, then divide by two which is 6.5 this means the 6th number and 7th are the two middle numbers.

If the amount of numbers in the list is even the median is the mean (average) of the two middle values in the list, while if the amount of numbers in the list is uneven it is simply the middle value.

How to calculate the median of a data set

Uneven List: { -7, -2, 26, 33, 40, 42, 55 }
33 is our median number, it is the middle number of the sorted list.

Even List: { -36,-18,-12, 40, 45, 65, 82, 91 }
The two middle values are 40 and 45, to get the median we get the average of these two. (40 + 45) /2 = 42.5

Mean

The mean is the average of the numbers in a data set. To calculate the mean, sum up all the numbers in the data set and divide the result by how many numbers there are. An interesting example of why the average works is how multiplying the average by how many numbers are in the set will give you the sum of the set.

How to calculate the Mean

Our data set is: { 3, 7, 11, 17, 23 }

  • Add all the numbers up: 3 + 7 + 11 + 17 + 23 = 61
  • There are 5 numbers in the set: 61/5 = 12.2
  • The mean is 12.2 for the set, to make sure the answer is correct, multiple the average by the amount of numbers in the data set
  • 12.2 X 5 = 61, with this we know we have the correct mean

If there are negative numbers within the set, adding a negative number is the exact same as subtracting the number.

How to calculate the mean with negative numbers

Our Data set is { 1, -3, 7, 11, -5, 4 }

  • The sum of 1 - 3 + 7 + 11 - 5 = 15
  • There are 6 numbers in the set
  • Mean is equal to 15/6 = 2.5
  • Again to double check multiple 2.5 by 6 = 2.5 X 6 = 15
  • 2.5 is our mean

Mode

The easiest way to find the mode of a data set is to put all the numbers in order and count how many of each number there is. The number that is in the set the most is the mode.

How to calculate the mode

{ 2, 4, 6, 7, 14, 14, 26, 32 } : 14 is our mode since it is the most common number

It is possible for there to be more the one mode, this is called bimodal, if there is more then two modes it is referred to as multimodal

{ 1, 4, 4, 4, 7, 8, 12, 12, 12, 27} our two modes are 4 and 12

Range

Range is the difference from the lowest value in the data set to the largest value, range can be affected excessively by an extremely small or large values.

How to calculate the Range of a data set

{4, 6, 21, 54, 65}: 65 - 4 = 61 is our range.