## Examples Using Average Formula

Let us solve some interesting problems using the Average formula.

**Example 1:** The marks obtained by 8 students in a class test are 12, 15, 16, 18, 20, 10, 11, and 21. Use the average formula and find out what is the average of the marks obtained by the students?

**Solution:**

To find: Average of marks obtained by 8 studentsMarks obtained by 8 students in class test = 12, 15, 16, 18, 20, 10, 11, and 21 Total marks obtained by 8 students in class test = = 123/8Using the average formula,Average = ÷ Average = ÷ 8 = 123/8 = 15.375

**Answer: The average of marks obtained by 8 students is 15.375.**

**Example 2:** The monthly incentives received by an employee for five months are: $21, $27, $31, $19, $22. Using the average formula, calculate the average incentive received by the employee for these five months.

**Solution:**

To find: Average for the given set.Given:Incentives for five months: Using Average Formula,Average = ÷ Average = ÷ 5= 120/5= 24

**Answer:** Average incentive received by the employee is $24.

**Example 3:** The weight of students in a class are listed here: . Using the average formula, calculate the average weight of students in the class.

**Solution:**

To find the average weight of students in a class.Given:Weights in lb: Number of students = 6Average = ÷ Average = ÷ = 330/6 = 55

**Answer: Average weight of students is 55 lb.**

## Average Percentage Return And Cagr

A type of average used in finance is the average percentage return. It is an example of a geometric mean. When the returns are annual, it is called the Compound Annual Growth Rate . For example, if we are considering a period of two years, and the investment return in the first year is 10% and the return in the second year is +60%, then the average percentage return or CAGR, *R*, can be obtained by solving the equation: × = × = × . The value of *R* that makes this equation true is 0.2, or 20%. This means that the total return over the 2-year period is the same as if there had been 20% growth each year. The order of the years makes no difference the average percentage returns of +60% and 10% is the same result as that for 10% and +60%.

This method can be generalized to examples in which the periods are not equal. For example, consider a period of a half of a year for which the return is 23% and a period of two and a half years for which the return is +13%. The average percentage return for the combined period is the single year return, *R*, that is the solution of the following equation: 0.5 × 2.5 = 0.5+2.5, giving an average return *R* of 0.0600 or 6.00%.

## Average Of Negative Numbers

If there are negative numbers present in the list, then also the process or formula to find out the average is the same. Lets understand this with an example.

**Example: **

Find the average of 3, 7, 6, 12, 2.

**Solution:- **The sum of these numbers

= 3 + + 6 + 12 +

= 3 7 + 6 + 12 2

= 12

Total Units = 5

Hence, average = 12/5 = 2.4

How does this whole idea of average or mean works? Average helps you to calculate how to make all the units present in a list equal.

Find the average of 6, 13, 17, 21, 23.

**Solution:**

= 6 + 13 + 17 + 21 + 23 = 80

Total units = 5

Hence, average = 80/5 = 16

**Example 3:**

If the age of 9 students in a team is 12, 13, 11, 12, 13, 12, 11, 12, 12. Then find the average age of students in the team.

**Solution: **

Given, the age of students are 12, 13, 11, 12, 13, 12, 11, 12, 12.

Average = Sum of ages of all the students/Total number of students

A = /9

A = 108/9

Hence, the average age of students in a team is 12 years.

**Example 4:**

If the heights of males in a group are 5.5, 5.3, 5.7, 5.9, 6, 5.10, 5.8, 5.6, 5.4, 6. Then find the average height.

**Solution: **

Given the height of males: 5.5, 5.3, 5.7, 5.9, 6, 5.10, 5.8, 5.6, 5.4 and 6

Average = Sum of heights of males/total number of males

A = /10

A = 56.3/10

A = 5.63

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## What Does It Mean When The Average Is Higher Than The Median

If the mean is greater than the median, the distribution is **positively skewed**. If the mean is less than the median, the distribution is negatively skewed.

How do you find an average? Average This is the arithmetic mean, and is **calculated by adding a group of numbers and then dividing by the count of those numbers**. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Why do we use an average?

The primary purpose of averages is **to measure changes over time in the same sample group or cohort**. It is in this application, or more so misapplications, by using averages for different purposes that the three most common errors occur. First, it is common in any data set for there to be outliers.

What is the purpose of finding an average? The purpose of taking the average of a set of data is **to give one a general idea of how the data set is acting or performing as a whole.**

## Similar Concepts Involving Averages

The weighted average calculator lets you assign weights to each number. A number weighting is an indicator of it’s importance. A common type of a weighted mean that is computed is the grade point average . To do this by hand, follow these steps:

Suppose the grades are an A for a 3 credit class, two B’s for the 4 credit classes and a C for a 2 credit class. Using the standard value of 4 for an A, 3 for a B and 2 for a C, the grade point average is GPA = / = 40/13 = 3.08

Note that the average calculator will compute the average for all values that are weighted equally. For a weighted average, such as GPA and other statistical applications, the weighted average calculator linked above is the tool you want to use. In statistics the mean is known as a measure of central tendency.

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## Why Are Averages Misleading

**Averages can be misleading for a number of reasons**. **They best represent evenly distributed bell curves**, where most results are found in the middle, and few on the extremities. But **even one very extreme point can change the average dramatically**, and so these anomalies are often excluded, but not always. Next, **humans tend to interpret averages as being perfect representations**, leading to a lack of desire to understand the nuances of the data. Lastly, averages are often used to predict **individual cases, which are often wildly inaccurate**.

## What Is The Meaning Of Average

The average is a numeric value which is a single representation of a large amount of data. The marks of the students of a class in a particular subject are averaged to give the average mark of the class. There is a need to know the performance of the entire class rather than the performance of each individual student. Here, the average is helpful. The average of a set of values is equal to the sum of the values divided by the individual values. Also, average is used in situations of changing values. The temperature of a place across the season is averaged to indicate the temperature of a place. The incomes of different employees in a company are averaged to know the income of the employees in a company.

It is sometimes difficult to make decisions based on one single data or a large set of data. Hence, the average value is taken and it helps to represent all the values in a single value

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## Can The Average Value Be Zero

The average value can be zero. For quantities having some positive values and some negative values, the sum of the values can equalize to zero. Let us consider an example of a set of values, 40, 90, -180, 20, 60, -30. The sum of these quantities is equal to zero. Hence the average value also is equal to zero

## What Is The Average Used For

The average is used to represent one single value for a given set of quantities. Further, it is always difficult to represent all the observations, and hence the average of the observations is taken to represent all the observations. Also in instances of changing values, the average of the values is taken to represent all the values. A few examples of average include, the average temperature of a place, the average marks of a student, and the average price of a stock.

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## What Is The Average Of Negative Numbers

If there are negative numbers present in the list of numbers, even then the process or formula to calculate the average remains the same.

Lets understand the concept of an average of negative numbers with an example.

Average examples: Find the average of 4, 7, 5, 10, 1.

Solution. Lets first find the sum of the given numbers.

= 4 + + 5 + 10 +

= 4 7 + 5 + 10 1

= 11

Total number of terms = 5

As we know the formula to calculate the average from the definition of average,

Average is equal to 1.2.

## Finding The Average When The Numbers In The Set Are The Same

When all the numbers in the set are the same, it is easy to find the average.

**Example #3**

Find the average of the following set of numbers:

6, 6, 6

Find the average of the following set of numbers:

12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 132

132/11 = 12

What can we conclude from example #3 and example #4?

When the numbers in the set are all the same, the average is just the number itself.

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## What Is The Correct Formula Of Average

Average, which is the arithmetic mean, and is calculated by **adding a group of numbers and then dividing by the count of those numbers**. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

What is the average difference? The average difference is **the sums of the difference between pairs of consecutive numbers**, to get the average, just divide that by the total number of pairs. COUNT function is used to count the number of values in the list.

What is the difference between sum and average?

Sum is a preferred measure when we just need total value or total items . Average is more like a statistical measure that is used to summarize the data or when we try to compare among groups where each group has different member counts.

Does average mean typical? An average is a single number that represents the middle of a data set. It is commonly interpreted to mean **the typical value**. Calculating averages facilitates easier understanding of and comparison between different data sets, particularly if there is a large amount of data.

## What Is The Mean Median And Mode

The *mean* is the number you get by dividing the sum of a set of values by the number of values in the set.

In contrast, the *median* is the middle number in a set of values when those values are arranged from smallest to largest.

The *mode* of a set of values is the most frequently repeated value in the set.

To illustrate the difference, lets look at a very simple example.

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## Why Do We Calculate Average

**We calculate averages because they are a very useful way to present a large amount of data**. Instead of having to trawl through hundreds or thousands of pieces of data, we have **one number that succinctly summarises the whole set**. While there are some problems with averages, such as outliers showing an inaccurate average, they are **useful to compare data at a glance**.

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## Can Median Be Considered As Average

No, the median is not considered as average. The average is the mean value of the data and is different from the median value of the data. Median is the middle value of a set of data arranged in increasing order. The median or middle value is also known as a central tendency. To find the measure of central tendency, we have to write the data points in increasing or decreasing order. Further, the calculation of the median depends on the number of data points. Let us look at the following two cases for the calculation of the median value.

**Case 1:**n is Odd. Here for the odd number of data points, there is only one middle data point. And the median of the data is the /2 observation.

**Case 2:**n is Even. Here for the even number of data points, there are two middle data points. And the median is the average of n/2 and observation.

For special cases of data having equally spaced data points, the average is equal to the median. Let us consider the numbers: 5, 10, 15, 20, and 25. The average of this data is equal to the sum divided by 5. Hence the average of the data is 75/5 = 15. And the median is the middlemost value and it is equal to 15. The average and the median for this data is equal to 15.

## Limitations Of The Arithmetic Mean

The arithmetic mean isn’t always ideal, especially when a single outlier can skew the mean by a large amount. Lets say you want to estimate the allowance of a group of 10 kids. Nine of them get an allowance between $10 and $12 a week. The tenth kid gets an allowance of $60. That one outlier is going to result in an arithmetic mean of $16. This is not very representative of the group.

In this particular case, the median allowance of 10 might be a better measure.

The arithmetic mean also isnt great when calculating the performance of investment portfolios, especially when it involves compounding, or the reinvestment of dividends and earnings. It is also generally not used to calculate present and future cash flows, which analysts use in making their estimates. Doing so is almost sure to lead to misleading numbers.

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## What Is Average In Maths

In math, the average is **the middle value of a set of numbers**. This isn’t to be confused with the median which is the middle of a set of numbers. The average is the middle value of the numbers. If you need to find the average of a set of numbers, you add them all together and divide by the amount of numbers.

Hereof, How do you explain average? In math, the average value in a set of numbers is the middle value, **calculated by dividing the total of all the values by the number of values**. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

Why is average called mean? Mean is **the central point of the set of values**. It is the average of values present in the data set. The central value which is called the average in mathematics is called the mean in statistics.

## Definition Of Average And Mean

**Average:** The term Average describes a value that should represent the sample. An average is defined as the sum of all the values divided by the total number of values in a given set. It is also known as the arithmetic mean. Let us consider a simple data to find the average.

Given, the set of values are 1, 2, 3, 4, 5.

Average = Sum of all the values/ Total number of values

Average = /5 = 15/5 = 3

**Mean:** A mean is a mathematical term, that describes the average of a sample. In Statistics, the definition of the mean is similar to the average.

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