# Mean, Median, Mode, and Range Statistics Calculator

Find the mean, median, mode, and range of a data set along with other information such as the total sum, count, min, and max values.

## Solution:

## How to Find Mean, Median, Mode, and Range

Mean, median, and mode are different ways to measure the center of a data set, this is referred to the central tendency. The range describes the variance between the numbers in the set, or the difference between the largest and smallest number.

These are used in summary statistics, which are used for summarizing a set of numbers.

### How to Find the Mean of a Data Set

In statistics the mean is the average value of a set of numbers and is referred to as the arithmetic mean. To find the mean, add up all of the numbers in the set to find the sum and then divide the sum by the number of values in the set.

**Example:** Find the mean for a set of numbers [1,2,3,4,5,6,7,8]

sum = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

mean = 36 ÷ 8 = 4.5

### How to Find the Median of a Data Set

The median is the middle number in an ordered set of numbers if the count of numbers in the set is odd. If the count of numbers in the set is even than the median is the average of the middle 2 numbers in the set. To find the median in a data set start by sorting the set in ascending order, then count the number of values in the set.

If the count is odd then divide the count by 2, then round up to get the index of the median in the set. Find the value at that index in the set to find the median.

**Example:** Find the median for a set of numbers [1,3,5,7,15,22,29]

count ÷ 2 = 3.5

middle index = 3.5 rounded up = 4

median = number at 4^{th} index = 7

If the count is even then find the two middle numbers in the set. Divide the count by 2 to find the index of one of the middle numbers. Add 1 to the first index to get the index of the second middle number. Find the values at those indexes, then add them together and divide by 2 to find the median.

**Example:** Find the median for a set of numbers [1,3,5,7,15,22,29,38]

count ÷ 2 = 4

lower middle index = 4

upper middle index = 4 + 1 = 5

number at 4^{th} index = 7

number at 5^{th} index = 15

median = (7 + 15) ÷ 2 = 11

### How to Find the Mode of a Data Set

The mode is the number that occurs most frequently in a set of numbers. To find the mode, count the number of times each number in the set occurs. The number with the greatest count is the mode. It is possible for a set of data to have more than one mode if each of the modes occur the same number of times.

**Example:** Find the mode for a set of numbers [1,2,2,2,3,4,5,5,5,6,7,7]

1 occurs 1 time

2 occurs 3 times

3 occurs 1 time

4 occurs 1 time

5 occurs 3 times

6 occurs 1 time

7 occurs 2 times

modes = 2 & 5

### How to Find the Range of a Data Set

The range is the difference between the smallest and largest numbers in a set of numbers. To calculate the range, find the largest and smallest numbers in the set, then subtract the smallest number from the largest number.

**Example:** Find the mode for a set of numbers [3,7,22,54]

smallest number = 3

largest number = 54

range = 54 – 3 = 51