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How to find the Median, Mean and Mode

How to find the Median, Mean and Mode

Mean, Median and Mode are the basic mathematical operations to find a specific value of n numbers. Mean is the center of the set of numbers given there. Mode is the number which has been repeated the most number of times in the series. The median of a set of numbers can be defined as the exact middle number in a sequence arranged properly. Finding the median of the number which is odd and for the even ones are two completely different processes. While finding the median for odd set of numbers is easy, finding median for even set of numbers requires an additional step. Similarly, we will also discuss as to how we can derive the Mean and Mode of a sequence of Numbers also.


Mean is also called the average of numbers or set of numbers provided in a chart. Let us say we have a set of number written here as { 3, 4, 8 } and we have to find the mean among them. so, what do we do? We would count the numbers first as to how many of them are there. In this case, there are three numbers. To find the mean, we would then add the numbers with one other. So, we get –  3 + 4 + 8 = 15. Adding these three numbers we get 15. Now this is the highest value of these numbers. So, mean would be – 15/3 = 5.

To find the mean of any number, we divide the sum of those numbers with total numbers and then we get the mean. Another example, let’s take another set of numbers – { 3, 4, 8, 5 }. Now we have a set of 4 numbers here. Their sum would be –  3 + 4 + 8  + 5 = 20. So mean here would be 20/4 = 5. This is how we calculate the mean of any set of numbers.


As mentioned above, the median is the exact middle number of any set of numbers arranged in a particular and increasing way. To find the median of any set of numbers, you should first arrange the numbers into increasing format. For example, let’s say you get the following set of numbers {5, 9, 4, 1, 3, 7, 6}, then what would be the median of the set of numbers here. First we would have to sort the set into increasing set of numbers here. So, the set becomes, {1, 3, 4, 5, 6, 7, 9 }. This is the first step. Now, finding the median of the number is different for odd and even numbers.

Odd Numbers – the above mentioned set {1, 3, 4, 5, 6, 7, 9 } is an odd set with 7 numbers here. So, we start counting with left and stop at 3 counts. Similarly from the right side also. The number 5 has 3 numbers on the left and right and stands at the exact middle of the sequence. So, 5 is the median here.

Even Numbers -Let’s take a set here, {1, 3, 4, 6, 7, 9 } with 6 numbers. So, to find the median of the set, we would take two middle numbers in 4 and 6 as there is no such middle ground here. So, to find the median, we add 4 and 6 and divide them with 2. So, 4 + 6 = 10/2 = 5. So, 5 is the median for this set.


Mode of any set of numbers can be defined as a number appearing most frequently in the set of numbers. For example, let us take this set of number – { 3, 2, 3, 3 , 6, 7, 7, 8, 7, 7}. In this set of 10 numbers, we see number of repetitions of 3 and 7. Mode would be the number which has been repeated the most number of time in the series of number. So, we arrange the number first – { 2, 3, 3, 3, 6, 7, 7, 7, 7, 8}. Here, the mode would be 7 as the repetition is 4 times while for 3, the repetition is 3 times only. For finding the mode, this is the best process to remember as to highest repetition.

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