About Average in Math
What is an Average?
An average is a single representation of a significant amount of data.
Examples such as the average temperature of a city, average incomes of employees in an organization, the average marks of students in a class, and so on, are a few everyday instances where averages come in handy. But how do we calculate the average of the given data? Let’s find out.
How do we Calculate the Average?
An average, also called the arithmetic mean, is calculated by dividing the sum of all the numbers by the total number of values in the data. In other words, the average is the ratio of the sum of observations to the total number of observations.
Average (Mean) = \( \frac{sum~of~observations}{Total~number~of~observations}\)
We will get more insights on this concept with the help of an example.
Example: Find the average of the given observations 10, 14, 15, 17 and 19.
Solution:
The stated observations are 10, 14, 15, 17 and 19.
And there are 5 observations.
Since we know, the formula for an average = \( \frac{sum~of~observations}{Total~number~of~observations}\)
= \( \frac{10~+~14~+~15~+~17~+~19}{5}\)
= \( \frac{75}{5}\)
= 15
Hence, the average of the given values is 15.
Rapid Recall
Solved Examples
Example 1:
Every month, Annie spends $150 on groceries, $120 on house rent, $110 on electricity and internet, $70 on transportation, and $90 for shopping and other purposes. Calculate Annie’s average monthly expenditure.
Solution:
As stated, Annie’s monthly expenses are:
Groceries: $150
House rent: $120
Electricity and internet: $110
Transportation: $70
Shopping and others: $90
So, the sum of all the expenses would be = 150 + 120 + 110 + 70 + 90
= 150 + 120 + 110 + 70 + 90
= $ 540
The total number of observations is 5.
Now, the average can be find by using Average = \( \frac{sum~of~all~expenses}{Total~count}\)
= \( \frac{540}{5}\)
= 108
So, Annie’s average monthly expenditure is $108.
Example 2:
In a poll of 300 people, it was discovered that a person spends an average of 2 hours per day on social media. Find out the total amount of time that they spent on social media.
Solution:
As stated:
The total number of people who participated in the poll = 300
Average number of hours spent on social media everyday = 2 hours/day .
Using the formula for average to find out the total time.
\( \frac{Total~number~of~time~spend}{Total~number~of~people}\) = Average
\( \frac{Total~number~of~time~spend}{300}\) = 2
Total amount of time spend = \( 2~\times~300\)
= 600
Therefore, the total time people spend on social media is 600 hours.
Example 3:
If the sum is 85 and the average is 5 for a group of n numbers, what is the value of n?
Solution:
It is given that sum of n numbers = 85
And average of n numbers = 5
Average = \( \frac{sum~of~observations}{Total~number~of~observations}\)
5 = \( \frac{85}{n}\)
\( n\) = \( \frac{85}{5}\)
\( n\) = 17
Hence, the value of \( n\) is 17.
The average of a given dataset is calculated by dividing the sum of the observations by the total number of observations in a dataset.
In a given dataset, the middle value is considered as the average whereas the value which occurred most frequently is known as the mode.
Yes. Sometimes the average may be negative if the given dataset has negative values.
Averages are used to represent a given set of quantities with a single value.
The average number of students in each class in a school, the average amount of milk consumed by people in a city and the average number of sales in a showroom, are a few real life instances where averages are used.