Formulas of Mean, Median, Mode and Range in Statistics

     The Mean, Median, Range, and Mode are the arithmetic average of a data set. This is found by additing the numbers in a data set and dividing by how many numbers there are. The median is the middle number in a data set, when the numbers are listed in either ascending to descending order. The mode is the value that occurs the most often in a data set, and the range is the difference between the highest and lowest value in a data set. Data actually have two type, there are group and ungroup of data. It's difference, group data is more than specific from ungroup data. Group of data usually have boundaries. Like between 10 until 15. Because that are difference, the formulas are difference too. So, you should know first which group data or ungroup data.

1. Mean ( Average of Data)

Formula for ungroup data

Explanation :

• xi = is the number i of data. 
• n = is count of data

Example : I have data like this :  2, 3, 1, 5, 6, 8, 10 . From that data, please search the mean (average)!

The Answer is : 2+3+1+5+6+8+10 = 35 . And the count of data is 7. So, the Mean is 35/7 = 5

Formula for group data

Explanation :

• xi = is the middle value of class i .
• fi = is the frequency of class i .

Example of group data

Middle value is 35 + 44 = 39,5...... So,the mean is 4330/60 = 72,16667

2. Median ( What middle value is)

Formula for ungroup data

Explanation :

• Lmd = is the location of median.
• n = is count of data.

Example :  I have data like this :  2, 3, 1, 5, 6, 8, 10 . From that data, please search the median!

- Answer - 

First, you have to sort the data first! So that data like this : 1, 2, 3, 5, 6, 8, 10 .

Then, the median is 7+1 / 2 = 4. That means the fourth data, so the median is 5. 

For some special case, i have data like this : 1, 2, 3, 5, 6, 7, 8, 10

So, the median is 8+1 / 2 = 4,5 . That means we must add the fourth and fifth values then divided by 2. So the median is 5+6 / 2 = 5,5 .

Formulas for search the middle data

Formula for group data

Explanation : 

• Md : is the symbol for median.
• Lmd : is the location of median. 
• Other variables can be seen in the example below.

Example for group data

Md = 74,5 + { ( 30 - 29)/17 } * 10 --------------  Md = 75, 08824

3. Mode (Data that often appears)

     No formula for ungroup data. You just need to calculate the same data. But, if the data so much, you can make it to group data with interval and Sturges formula.

Formula for group data

Explanation :

• Mo : the symbol for mode.
• Other variables can be seen in the example below

Example for group data

Md = 74,5 + { 6 / (6 + 6) } * 10 ------------------ Mo = 79,5

4. Range

     The range is the difference between the highest and lowest value from data. You just need find the highest and lowest values. Then substract the lowest value from the highest value. No formula for range, just substract it like general.

     That is all the formulas for Mean, Median, Mode, and Range. Basically, all fixed on the calculate formula. You must know every variables in the formulas, so you can insert the value correctly. Happy study... i hope you understand this before we continue the next lesson.