How to Calculate Mean

How to calculate mean? In Mathematics, mean is nothing but the average of certain values or a set of numbers. It is easy to calculate the mean value of a given set of values. We need to add all the values then divide the answer by the number of values. Also, it is possible that values are repeated in the data set, but we need to make sure that all the values are counted, to find the mean.

The formula of the mean is given by:

In other words, mean is the way of finding the sum divided by the count of the values. It is applicable when we need to divide something into equal numbers. For example, there are 3 baskets that have a different number of apples such as 3, 4 and 5, respectively. To put an equal number of apples in each basket, we need to find the mean of all the apples.

Mean of apples = (3+4+5)/3 = 12/3 = 4

Therefore, we can put 4 apples in each basket.

Learn more:

• How to Find Median
• How to find Mode

How to Find Mean of Negative Numbers

If the given set of numbers or values include the negative numbers, then we have to add all the values with their respective sign and then divide by the number of values. As we know, the addition of negative numbers will lead to subtraction.

Example: Find the Mean of -3, 4, 9, -11, 14.

Adding all the given numbers we get;

Sum = (-3+4+9-11+14) = 13

Total number of values = 5

Therefore,

Mean = 13/5 = 2.6

Mean in Statistics

In statistics, the mean is the value used to summarize the given data set. It measures the center of the data, hence called a measure of central tendency. Mean is calculated to find the average of different scenarios in real life, such as an average number of people having a TV in a city, average marks obtained by students in a class, etc.

Example: In a class, there are five students who have scored 70, 20, 80, 60 and 70 marks in a subject. What is the mean of all the marks obtained by the students?

Solution:

Given, the marks obtained by the five students are 70, 20, 80, 60 and 70, respectively.

Mean = Sum of all the marks ÷ Total number of students

Mean = (70+20+80+60+70) ÷ 5

Mean = 300 ÷ 5

Mean = 60

Therefore, the mean of the marks obtained by the students is 60.

Solved Examples

Let us solve some questions to find the mean.

Q.1: Find the mean of 2, 1, 2, 4, 5, 4.

Solution: Given, 2, 1, 2, 4, 5, 4

Mean = Sum of Values ÷ Total number of Values

Sum of values = 2+1+2+4+5+4=18

Total number of values = 6

Therefore,

Mean = 18/6 = 3

Q.2: Calculate the mean of 4.5, 5, 2, 2.5, 3.5.

Solution: Given, 4.5, 5, 2, 2.5, 3.5.

Mean = Sum of Values ÷ Total number of Values

Sum = 4.5+5+3.5+2+2.5=17.5

Total values = 5

Therefore,

Mean = 17.5 ÷ 5 = 3.5

Q.3: Find the mean of 13, 18, 13, 14, 13, 16, 14, 21, 13.

Solution: Given, set of values are 13, 18, 13, 14, 13, 16, 14, 21, 13

Mean = Sum of Values ÷ Total number of Values

Sum = 13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13 = 135

Total values = 9

Therefore,

Mean = 135/9 = 15

Try Yourself

Find the Mean of the following values:

• 1, 2, 4, 7
• 8, 9, 10, 11, 12
• 4, 6, 8, 9, 22, 83, 98, 45, 87,10
• 10, 10, 20, 40, 70.

How to Calculate Mode and Median

Mode and median are also the measures of central tendency, apart from the mean. Median is used to evaluate the central or middle value of the given data set when arranging data in order whereas mode gives the value that is repeated frequently.

Example: Find the mode and median of 13, 18, 13, 14, 13, 16, 14, 21, 13.

Let us first arrange the given data in ascending order.

13, 13, 13, 13, 14, 14, 16, 18, 21

Now as we can see, there is a total of 9 values. Thus, the middle value will be the 5th value.

Hence, median = 5th value = 14

Now, as we can see, the value 13 is repeated here 4 times. Therefore, it has more frequency.

Hence, mode = 13