Statistical Techniques in Sales Forecasting

This article uses statistical techniques to conduct sales forecasting in a business organization. Sales forecasting predicts future level of sales in a business from past sales data. Business managers rely on this data, which has been kept over a given period of time since it occurred, to predict the future.

What are statistical techniques?

Statistical techniques are a method of sales forecasting that is based on historical sales data, for example the past 12 months.

Statistical analysis investigates past sales data with an attempt to identify key features of the data such as average sales, central point of sales, frequency of sales, range of sales, variation of sales and changes in sales.

Interpreting and analyzing previous statistical data can help business managers to make well-informed assumptions what future sales results might be by comparing them with the past.

Methods of statistical techniques in sales forecasting

There are several statistical techniques that can be used to analyze the past sales data over the last 12 months. The most common thirteen methods of descriptive statistics used in business management have been grouped in five categories:

1. AVERAGE. Shows the center point of sales data:

a. Arithmetic mean – Average monthly sales

b. Median – Middle value of monthly sales

2. FREQUENCY. Shows how often particular sales occurred:

a. Mode – Most frequent monthly sales

b. Frequency data – Most frequent average monthly sales

c. Grouped frequency data – Frequency of monthly sales within different groups of sales data

3. DISPERSION. Shows how widely monthly sales are spread:

a. Range – Difference between the highest and lowest monthly sales

b. Quartiles – Distribution of monthly sales into 4 equal groups within sales data

c. Inter-quartile range – Range of the central 50% of the sales data

4. DEVIATION. Shows distance of monthly sales from the center point (mean):

a. Variance – Spread of monthly sales from the mean

b. Standard deviation – Average difference between monthly sales and the mean

c. Mean deviation – Average of differences between monthly sales and the mean

5. CHANGE. Shows how monthly sales changed over time.

a. Index numbers – Changes in monthly sales

b. Weighted index numbers – Changes in monthly sales when months are of unequal importance

Sales forecasting is done in order to help the business identify in advance any problems and opportunities related to sales of products.

Example of using statistical techniques in a business

Let’s say that your small business generated USD39,000 in sales revenue in 2020. Over the period of two years, monthly sales were never constant; hence sales revenue was different each month.

The table below shows the exact amounts of sales revenue your business generated each month in 2020 and 2021:

MONTH:	SALES REVENUES (2020):	SALES REVENUE (2021):
JANUARY	USD5,000
FEBRUARY	USD2,000
MARCH	USD3,000
APRIL	USD1,500
MAY	USD6,500
JUNE	USD7,000
JULY	USD5,500
AUGUST	USD5,000
SEPTEMBER	USD6,000
OCTOBER	USD8,000
NOVEMBER	USD2,500
DECEMBER	USD5,000
TOTAL:	USD57,000

1. AVERAGE. It shows what the center point of the sales dataset is.

a. Arithmetic mean – Average monthly sales. This simple average shows the average monthly sales revenue in a period of one year. It is the sum of all monthly sales revenues divided by 12 months.

Arithmetic mean = (x₁ + x₂ + (…) + x_n) / n

2020: Arithmetic mean = USD3,250

2021: Arithmetic mean = USD4,750

The business generated USD4,750 per month on average in 2021. The mean value of monthly sales revenue increased from USD4,750, or by USD6,942 in 2022.

b. Median – Middle value of monthly sales. Median is the middle value of monthly sales revenue. In our case, there is an even number of items (12 months) in a dataset which means that the median sales revenue will be the midpoint between the two central items (the 6^th month and the 7^th month in ascending dataset).

Median (even) = (1^st middle value + 2^nd middle value) / 2

2020: Median (even) = (USD3,500) / 2 = USD5,000 + USD5,000

The median sales revenue generated by the business is USD5,000 per month in 2021. The median value of monthly sales revenue increased from USD5,000, by USD3,500 for 6 months in 2020 (and less than USD5,000 for 6 months in 2021 (and less than USD7,143 in 2022.

2. FREQUENCY. It shows how often particular sales occurred.

a. Mode – Most frequent monthly sales. The mode is the most frequently earned sales revenue in the period of 12 months.

2020: The mode of 2020’s results is USD1,500 in sales revenue more times than any other value of sales revenue.

2021: The mode of 2021’s results is USD5,000 in sales revenue more times than any other value of sales revenue.

b. Frequency data – Most frequent average monthly sales. Frequency data is used to show the average monthly sales revenue that appears the most frequently among all sales revenue values.

Mean frequency = ∑fx / ∑f

Where:

x – Monthly sales revenues

f – Frequency for monthly sales revenues

∑x – Sum of monthly sales revenues

∑f – Sum of frequencies for all monthly sales revenues

∑fx – Sum of monthly sales revenues x Frequency

The following table shows frequencies of monthly sales revenues in 2020:

Sales Revenue (x):	Frequency (f):	fx:
USD1,000	1	1000
USD3,500	2	7000
USD4,500	1	4500
USD5,500	1	5500
USD3,250 The following table shows frequencies of monthly sales revenues in 2021: Sales Revenue (x): Frequency (f): fx: USD2,000 1 2000 USD3,000 1 3000 USD5,500 1 5500 USD6,500 1 6500 USD8,000 1 8000 ∑f = 12 ∑fx = 57,000 2021: Mean frequency = USD3,250. The result of mean frequency in 2021 shows that the average monthly sales revenue generated the most often was USD7,143 in 2022. c. Grouped frequency data – Frequency of monthly sales within different groups of sales data. Grouped frequency data shows how different values of monthly sales revenue appear within different groups of sales revenue in the dataset of 12 months. Mean frequency = ∑fx / ∑f The following table shows grouped data in 2020: Sales Revenue (x): Midpoint: Frequency (f) fx: Cumulative Frequency: 2,000 5,000 5 4,000 9,000 8 6,000 15,000 11 8,000 7,000 12 TOTAL: ∑f = 12 ∑fx = 36,000 2020: Mean frequency = USD3,000 The mean frequency in this business in 2020 is USD3,000. Modal group is the group with the highest frequency among all groups in the dataset. The modal group in this business in 2020 is the first group with 5 sales revenues between USD2,000. The following table shows grouped data in 2021: Sales revenue (x): Midpoint: Frequency (f) fx: Cumulative frequency: 2,000 2,000 2 4,000 6,000 4 6,000 25,000 9 8,000 21,000 12 TOTAL: ∑f = 12 ∑fx = 54,000 2021: Mean frequency = USD4,500 The mean frequency in this business in 2021 is USD4,500. Modal group is the group with the highest frequency among all groups in the dataset. The modal group in this business in 2020 is the third group with 5 sales revenues between USD6,000. 3. DISPERSION. It shows how widely monthly sales are spread from the lowest to the highest monthly sales revenue. a. Range – Difference between the highest and lowest monthly sales. Range is the difference between the highest and the lowest monthly sales revenue over the period of 12 months. Range = Highest result – Lowest result 2020: Range = USD500 = USD8,000 – USD6,500 The range of monthly sales revenue in 2020 is USD6,500. The difference between the highest and the lower monthly sales revenues in 2020 and in 2021 is the same meaning that there is the same spread in monthly sales revenues in 2021 comparing with 2020 2022: The range of monthly sales revenue might also be USD3,500. It means that half of the monthly sales revenues were below USDUSD3,500. Q1 which is USD500 and the median (Q2) which is USD1,500. Q3 which is USD7,000. In this case, Q3 is the middle value between 9th and the 10th value. Let’s interpret the numbers that represent quartiles. 1. Monthly sales revenue of USD1,500 is the median of the lower half of the score set in the available data. It tells us that 25% of the monthly sales revenues are less than USD3,500 (Q2, or the median, or medium quartile) represents the second quartile and is the 50th percentile. USD3,500 and 50% of the monthly sales revenues are above USD4,750 (Q3, or higher quartile) represents the third quartile and is the 75th percentile. USD4,750 and 25% of the monthly sales revenues are above USD5,000. It means that half of the monthly sales revenues were below USDUSD5,000. Q1 which is USD1,500 and the median (Q2) which is USD2,750. Q3 which is USD8,000. In this case, Q3 is the middle value between 9th and the 10th value. Let’s interpret the numbers that represent quartiles. 1. Monthly sales revenue of USD2,750 is the median of the lower half of the score set in the available data. It tells us that 25% of the monthly sales revenues are less than USD5,000 (Q2, or the median, or medium quartile) represents the second quartile and is the 50th percentile. USD5,000 is the median of the whole dataset – 50% of the monthly sales revenues are below USD5,000. 3. Monthly sales revenue of USD6,250 is the median of the higher half of the score set in the available data. It tells us that 75% of the monthly sales revenues are below USD6,250. c. Inter-quartile range – Range of the central 50% of the sales data. It is the range of monthly sales revenues between the upper quartile (Q3) and the lower quartile (Q1) in the year. It shows the range of the middle 50% of the monthly sales revenues while ignoring the bottom 25% and top 25% of the results. Inter-quartile range = Upper quartile (Q3) – Lower quartile (Q1) 2020: Inter-quartile range = USD1,500 = USD3,250 which is the difference between the upper quartile (Q3) and the lower quartile (Q1). It means that the range of the middle half of monthly sales revenues is USD6,250 – USD3,500 The inter-quartile range in USD3,500. 2022: If the business increases its inter-quartile range next year by 7.7%, it will be , the median will be USD3,250 2021: Arithmetic mean = USD2,051 2021: Standard Deviation = √4,204,545 = USD3,250 is USD2,051. The typical (average) deviation of monthly sales revenues in 2021 from the arithmetic mean of USD2,073. This means that the average distance of all 12 monthly sales revenues from the arithmetic mean is USD3,250 2021: Arithmetic mean = USD20,500 2021: Sum of absolute deviations = USD1,864 2021: Mean deviation (for the sample) = USD1,864 in 2020 is lower than the standard deviation of USD1,818 in 2021 is lower than the standard deviation of USD3,500	USD500	USD1,000	USD1,500	USD3,500	USD5,000	USD7,000	USD4,500	USD5,500	USD4,000	USD1,500	USD1,500	USD39,000	USD57,000 / USD3,500	USD500	USD1,000	USD1,500	USD3,500	USD5,000	USD7,000	USD4,500	USD5,500	USD4,000	USD1,500	USD1,500	USD39,000	USD$57,000	R = 2,267.35	R x W = 2,597.03

A. Weighted Average of Relatives Method:

Weighted Index Number P₀₁ = (ΣR x W)/ ΣW

Weighted Index Number P₀₁ = 2597.03 / 15 = 173.14

The index number of 173.14 shows that the monthly sales revenues, when different months are having different importance throughout the year, increased by 73.14% for each month between 2021 compared to 2020.

In summary, different methods of statistical techniques in sales forecasting based on historical sales data can help to analyze the past sales in order to make assumptions for the future. It helps to identify key features of the data such as average sales, central point of sales, frequency of sales, range of sales, variation of sales and changes in sales to help business managers make well-informed predictions regarding what future sales results might be referring to the past.