Simple average vs weighted average

Data analysis is an important aspect of several functions such as economics, accounting, management and finance. Data analysis employs several tools – statistical and mathematical tools being one of them. Averages is one such mathematical analysis tool. It is essentially a single value that summarizes or represents a set of values. An average can have different meanings in different applications.

This article looks at meaning of and differences between two types of averages –simple average and weighted average.

Definitions and explanations

Simple average:

As the name suggests, simple average of a set of values is determined by dividing the sum total of all the values by the number of values in the set.

The formula of simple average can be expressed as follows:

Simple average = (Total of x¹ ₊ x²+x³…..+xⁿ)/n

where;

• x = values in the set
• n = number of values in the set

For example, say ABC Inc. has 5 different items in its stock and wishes to know the average price of its stock. The simple average can be calculated as below:

Sr No	Stock item name	Cost price (in USD)
1	Copper	10
2	Brass	12
3	Iron	9
4	Aluminium	20
5	Plastic	8
	Total	59
	No. of items	5
	Simple average (Total/no.of items)	11.80

 The main benefit of simple average is its ease of calculation. A drawback of simple average method is however that it may not be an accurate representation of an average especially if values in the set have varying importance attached to them.

Thus, simple average is an effective method to calculate the average of a set of values in which each value is of equal importance. In other cases, use of weighted average may be more accurate, as detailed below.

Weighted average

Weighted average is a means of determining the average of a set of values by assigning weightage to each value in relation to their relative importance/significance.

The formula of weighted average can be expressed as follows:

Weighted average = (Total of x¹w¹₊ x²w²+x³w³…..+xⁿwⁿ)/(Total of w¹ +w²+w³….+wⁿ)

where;

• x = values in the set
• w = weightage of each value in the set
• n = number of values in the set

For example, let’s continue the same example as above. While ABC Inc has 5 different items in its stock, they are present in different quantities in stock. The quantities in which they are present will become the ‘weights’ and thus a weighted average calculation would be more accurate to calculate the average price of its stock. The weighted average can be calculated as below:

Sr No	Stock item name	Cost price (in USD) [A]	Quantity in stock (in kg) [B]	Weighted cost [A * B]
1	Copper	10	9	90
2	Brass	12	22	264
3	Iron	9	31	279
4	Aluminium	20	11	220
5	Plastic	8	27	216
	Total		100	1069
	Weighted average (Weighted cost/total of weights)			10.69

As can be seen, the weighted average cost arrived at differs from the simple average cost due to the introduction of quantities in the data set.

Weighted average method is opted for when values in a set are all not of equal importance. Thus, by taking into consideration the relative importance of each value, the weighted average method seeks to equate all the values comprised in the set. This makes weighted average method a more complex but more accurate calculation method than simple average.

Difference between simple average and weighted average

The difference between simple average and weighted average has been detailed below:

1. Meaning

• Simple average is the average of a set of values calculated with each value being assigned equal importance or weightage.
• Weighted average is the average of a set of values calculated by giving weightage to the relative importance of each value.

2. Formula numerator

• In simple average calculation, the numerator of the formula is the sum total of all the values in the set.
• In weighted average calculation, the numerator of the formula is the sum total of – the values in the set multiplied by the weightage assigned to each value.

3. Formula denominator

• In simple average calculation, the denominator of the formula is the total number of values in the set.
• In weighted average calculation, the denominator of the formula is the sum total of all the weights assigned to the values in the set.

4. Weights assigned

• In simple average calculation, weights are not assigned to each value.
• In weighted average calculation, weights are assigned to each value in relation to their specific importance/relevance.

5. Useful when

• Simple average calculation is useful in simpler data analysis when all values are equally important. It is more relevant in simple mathematical analysis.
• Weighted average calculation finds more relevance in accounting and financial calculations such as – weighted average cost of inventory, weighted average cost of capital.

6. Indication of

• Simple average is an indication of arithmetical mean or center point of the set of values.
• Weighted average on the other hand does not necessarily indicate this. It would be more tilted towards the values which have been assigned a greater weight in the set.

7. Ease of calculation

• Simple average is easier to calculate.
• Weighted average is more complex to calculate than simple average.

8. Accuracy

• Simple average is a less accurate method of average calculation especially in more complex sets of data.
• Weighted average considers the relative importance of all values and thus is a more accurate representation of the average of a set.

Simple average versus weighted average – tabular comparison

A tabular comparison of simple average and weighted average is given below:

Simple average vs Weighted average
Meanings
Average of values computed by assigning equal importance/weightage to each value	Average of values computed after taking into account the relative importance/weightage of each value
Formula numerator
Total of all values	Total of weighted values (i.e., total of values after assigning importance/weightage to each value)
Formula denominator
Number of values	Total of weights assigned to values
Weights assigned
Weights are not assigned	Weights are assigned to values
Useful when
Used in simple data analysis situations where each value is of equal importance or weightage	Used in relatively complex data analysis situations where each value requires a significantly different importance or weightage
Indication of
Arithmetical mean or center point	Titled towards the values with greater importance or weightage
Ease of calculation
Easy to compute	Complex as compared to simple average
Accuracy
Less accurate	More accurate as compared to simple average

Conclusion – simple average vs weighted average:

Both simple and weighted average methods are acceptable methods of calculating the average of a set of values. However, it is primarily their utility in various applications that separates them. While simple average is more useful in simple mathematical calculations, weighted average has a wider range in accounting and financial applications. This makes weighted average a more relevant analysis tool for business applications.