How to calculate average

The types of averages

There are several types of averages, the main types are:

Mean: This is the most common type of average and is calculated by adding all the numbers in a set together and then dividing by the number of items in the set.

Median: This is the middle value in a set of numbers when they are arranged in order.

Mode: This is the number that appears most frequently in a set of numbers.

Harmonic Mean: This is the reciprocal of the arithmetic mean of the reciprocals of the given set of numbers.

Root Mean Square: It is the square root of the average of the squares of a set of numbers.

How to calculate the mean avearage

The mean is genrally the most common type of average used. To calculate the mean average of a set of numbers, you need to:

Add all the numbers in the set together.

Divide the sum by the number of items in the set.

For example, if the set of numbers is {1, 2, 3, 4, 5}, you would add them together to get 1 + 2 + 3 + 4 + 5 = 15.

Then divide the sum (15) by the number of items in the set (5) to get the mean average: 15 / 5 = 3.

Another way to calculate mean is to use the formula : Mean = Sum of all numbers / Total numbers

How to calculate the median average

Median is a measure of central tendency and useful when the data set is skewed (not symmetric) or when the data set has outliers.

To calculate the median average of a set of numbers, you need to:

Arrange the numbers in the set in numerical order.

If the set has an odd number of items, the median is the middle number.

If the set has an even number of items, the median is the average of the two middle numbers.

How to calculate mode

Mode is a measure of central tendency and it is used when the data set has categorical variables or when you want to know the most frequent item in a data set.

To calculate the mode of a set of numbers, you need to:

Arrange the numbers in the set in numerical order.

Count how many times each number appears in the set.

The number(s) that appears most frequently is the mode.

For example, if the set of numbers is {5, 8, 2, 9, 1, 6, 7, 8, 8}, you would arrange them in numerical order to get {1, 2, 5, 6, 7, 8, 8, 8, 9}. The number 8 appears 3 times, which is the most frequent. Therefore, the mode of this set is 8.

It's important to note that a set of numbers can have multiple modes, if no number is repeated is said to have no mode.

How to calculate weighted mean

Weighted mean is a measure of central tendency and it's useful when some items in the data set are more important than others.

1. Assign a weight to each number in the set, which represents how much importance or influence that number should have in the final average.
2. Multiply each number by its corresponding weight.
3. Add up all the products from step 2.
4. Divide the sum from step 3 by the sum of all the weights.

For example, if the set of numbers is {5, 8, 2} and the corresponding weights are {1, 2, 3}, you would first multiply each number by its corresponding weight: 5 * 1 = 5, 8 * 2 = 16, and 2 * 3 = 6.

Then, you would add up the products: 5 + 16 + 6 = 27.

Finally, you divide the sum of the products by the sum of the weights. In this case, sum of the weights is 1+2+3 = 6, so the weighted mean is 27/6 = 4.5

How to calculate Geometric Mean

Geometric Mean is a measure of central tendency and it's particularly useful when you are dealing with rates of growth or compounding, or when your data set contains zero or negative values.

To calculate the geometric mean of a set of numbers, you need to:

Multiply all the numbers in the set together.

Take the nth root of the product, where n is the number of items in the set.

For example, if the set of numbers is {5, 8, 2}, you would first multiply all the numbers together: 5 * 8 * 2 = 80.

Then, you would take the cube root of the product, since there are 3 numbers in the set: ∛80 = 4.

Another way to calculate geometric mean is using the formula: Geometric Mean = (Product of all numbers)^(1/n) where n is the total number of items.

How to calculate Harmonic Mean

Harmonic Mean is a measure of central tendency and it's particularly useful when you are dealing with rates or ratios, or when you want to find an average that is less affected by outliers or extreme values.

To calculate the harmonic mean of a set of numbers, you need to:

Take the reciprocal of each number in the set.

Add up all the reciprocals

Divide the total number of items in the set by the sum of the reciprocals.

For example, if the set of numbers is {5, 8, 2}, you would first take the reciprocal of each number: 1/5, 1/8, and 1/2.

Then, you would add up the reciprocals: 1/5 + 1/8 + 1/2 = 11/40.

Finally, you would divide the number of items in the set (3) by the sum of the reciprocals (11/40): 3 / (11/40) = 120/11 = 10.91

Another way to calculate Harmonic Mean is using the formula: Harmonic Mean = n / (1/x1 + 1/x2 + 1/x3 + ... + 1/xn) where n is the total number of items in the set and x1, x2, x3, ..., xn are the numbers in the set.

How to calcualte Root Mean Square (RMS)

Root Mean Square is a measure of central tendency and it's particularly useful when you are dealing with measurements of power or energy, or when you want to find an average that is less affected by outliers or extreme values.

To calculate the root mean square (RMS) of a set of numbers, you need to:

Square each number in the set.

Add up all the squared numbers.

Divide the sum from step 2 by the number of items in the set.

Take the square root of the result from step 3.

For example, if the set of numbers is {5, 8, 2}, you would first square each number: 5^2 = 25, 8^2 = 64, and 2^2 = 4.

Then, you would add up the squared numbers: 25 + 64 + 4 = 93.

Next, divide the sum (93) by the number of items in the set (3) to get 31.

Finally, take the square root of the result (31) to get the RMS, which is 5.5 in this case.

Another way to calculate RMS is using the formula: RMS = √(x1^2 + x2^2 + x3^2 + .... + xn^2) / n where n is the total number of items in the set and x1, x2, x3, ..., xn are the numbers in the set.