Simple average and weighted average are two widely used methods of allocating averages of data sets.
Both methods are useful with some pros and cons for each. Let us discuss what are these methods and their key differences.
What is a Simple Average?
A simple average refers to a number that is derived by adding all numbers in a data divided by the count or figures in the data set.
It can also be defined as the ratio of the sum of numbers divided by the total values available in the data set.
It is an arithmetic expression that expresses the value of a data set with a single value. Average represents different properties in a data set.
For instance, if the data set values increase with an equal number, the change in the average will also be a constant value.
Simple average is the basic form of arithmetic average. It has different variations like mode, median, weighted average, etc.
How Does Simple Average Work?
The average value is the representation of the total values in a data set. It has different applications in mathematics, accounting, statistics, and other fields.
For instance, we can use the average formula to calculate the average age of the citizens of a city or country. It can be used as a sampling representation of a large set of data as well.
Simple average can be used for positive and negative integer values. For example, if a data set included negative integers, it will offer a negative integer as the average of the data set.
Steps to Calculate Simple Average
Let us first see the formula to calculate the simple average.
Average = Sum of Values / Total Number of Values
Suppose we have values a1, a2, a3, …. an. There is a total “n” number of values. Then,
Average = (a1 + a2 + a3 + …. an) / n
We can calculate the average of a given data set with the help of a few simple steps.
The first step is to determine the range of data to be included in the formula. The numerator includes all data set values that need to be averaged.
For example, if a small business wants to calculate the average sales of the last month. The data set will include sales figures for the last 30 days.
The second step is to simply take the sum of all values in the data set. It simply means to add all values from the first number to the last one in the data set.
In our example, it should be the sum of the sales of the last 30 days for the business.
The third step is to determine the total number of values used in the numerator. It means the denominator is the total number of figures used in the numerator.
In our example, it is the data set of 30 days, hence it will be 30.
The last step is to complete the division and calculate the average. The resulting figure will be the simple average figure of the data set used.
Suppose a small retail outlet ABC wants to calculate the average sales of the last week. Its sales per day for the last 7 days are: $ 300, $ 350, $ 180, $ 270, $ 220, $ 180, and $ 400.
We can calculate average sales for the last 7 days using the average formula.
Average Sales = ($ 300 + $ 350 + $ 180 + $ 270 + $ 220 + $ 180 + $ 400)/7= $ 1,900/7
Average Sales = $ 271.4
Pros and Cons of Using Simple Average
Using simple average has several pros and cons.
Advantages of using simple average are:
- It is easy to calculate and understand.
- It offers the analytical view of a data set.
- It derives several variations from its basic versions.
- It can be used widely in education, businesses, accounting, and finance concepts easily.
Disadvantages of simple average are:
- It can only be used where changes in the data set values are consistent.
- It does not offer the interpretation of the changes in the values.
- It may not be suitable for a large set of data.
What is Weighted Average?
The weighted average refers to the average value assigned proportionally in a data set. It means it is the average taken after assigning importance to each value in the data set.
Unlike the simple average, the weighted average does not assign equal or identical value to each number in the range of data.
It uses a relevancy tool to find the weighted average. It assigns a weight to each number according to the value or importance of that figure. It means each value will have a predetermined multiplier before the calculation.
Usually, the total weightage of the data set equals 1 or 100% when used in percentage terms. However, it can go beyond 100% in some cases as well.
How Does Weighted Average Work?
Weighted average assigns a percentage, proportion, or weightage to values in a data set. It means the weighted average is the process of assigning importance to each value in a data set.
Unlike the simple average, it does not assign the arithmetic average equally to all values. It is a refined process of calculating averages than the simple average method.
Steps to Calculate Weighted Simple Average
The weighted average can be calculated by using this formula:
Weighted Average = (a1w1 + a2w2 + a3w3 + …. an wn) / wn
Here a1, a2, a3, …. an are average values multiplied by w1, w2, w3… wn by their assigned weights. Wn is the sum of weightages assigned.
Using the formula above, the weighted average can be calculated in a step-by-step approach.
The first step is to determine the range of the data set. The weighted average can be calculated for all values in a large data set using software or spreadsheets.
However, it is also possible to use sampling from a large data range with consistent values.
The second step is to assign weightage to each value selected from the data range. It can be in a percentage form or decimal point. The total assigned weightage should be equal to 100% or 1.0 respectively.
The third step is to multiply the assigned weightages to each data set.
The final step is to add the calculated average weightages to find the total weighted average of the data set.
Note: If you use the assigned weightage in percentage terms, then you do not need to divide the weighted average by the sum of weightages.
Suppose a class teacher wants to calculate the weighted average of the score of the students for all four assessments held during the year.
A student S1 scores 55, 68, 73, and 90 in all four assessments. The teacher wants to allocate more weightage to the final and midterm assessments respective.
The weightages assigned are 15%, 15%, 20%, and 50% respectively.
The weightage average score of the student S1 can be calculated as:
Weighted Average = 55 * (15%) + 68 * (15%) + 73 * (20%) + 90 * (50%)
Weighted Average = 8.25 + 10.2 + 14.6 + 45.0 = 78.05
A simple average would have given a score of 71.5 only.
Pros and Cons of Using Weighted Average
Weighted average has several pros and cons as compared to other methods.
Pros of using weighted average include:
- It offers a realistic approach to calculating the average value of a large data set.
- It eliminates the distortions due to unusual highs and lows in a data set.
- It reduces the impact of volatility and sudden changes in the data set.
- It can help calculate averages depending on the importance of each data value.
Cons of using weighted average are:
- Assigning suitable weightage is difficult as it is prone to bias.
- It can be a complex method to assign weightages to a large data set.
- It may not represent a suitably weighted average when the sampling method is used for a large data set.
Simple Average Vs Weighted Average – Key Differences
The simple average and weighted average methods have some key differences in approach and practical applications.
Let us summarize these key differences here.
The simple average method is the process of allocating equal weight to values in a data set.
The weighted average method is the process of assigning weighted or proportioned values to numbers in a data set.
Simple average is the basic method used in simple calculations. It is useful for data sets where the change in values is consistent.
The weighted average can be used in complex statistical, accounting, and financial models where values fluctuate randomly.
Simple average assumes all values in the data set are equal to or close to the central value of the data. If there are extreme highs and lows in the data set, it will not provide accurate average figures.
The weighted average can assign a percentage value to each extreme or fluctuating value in the data set. Therefore, each input value can be assigned a unique weightage.
Simple average is easy to calculate and understand. It can be used in simple arithmetic average problems easily.
The weighted average is useful in accounting, finance, and statistical models where data values are inconsistent or require attributions according to their importance.
The simple average method does not absorb the effects of sudden changes in input data. It will offer distorted results if there are extreme highs or lows in the data set.
The weighted average is prone to the bias of assigning weightages. It can be a complex and difficult task to allocate weightages to all values in a large data set.