Modeling growth in any application requires a mathematical model based on parameters affecting growth.

Those parameters may include marketing budget, product development, number of increasing organic customers, historical growth, and a large variety of other factors depending on the type of growth being modeled.

Modeling growth extrapolates from past data into future data. Once a model is presented that has historical merit, that is approximate growth curves fit the data, the future data can be predicted with accuracy.

Growth models can be very mathematically complex, and rely on a large number of data variables. Mathematical models, however, are data generating not data analysis tools. Once the data figures are extracted from a model, with their correct parameters, the data can be manipulated in a spreadsheet to project meaningful information for data analysis.

### Using percentages in Data Analytics for Growth

For meaningful data analysis, it’s far more important to determine growth in a percentage so that it can be compared against other parameters for effective conclusions.

To explain this point, if data increases from 100 to 110, it’s obvious this is a 10% increase, however, data increasing from 1000 to 1010, is only a 1% increase. 10/1000 = 1/100 = 1%. For the same numerical increase, the percentage increase is 10 times lower.

When numerical data from a growth model is represented in a table, it’s a simple matter of applying a calculation to the data to convert it to percent.

### Calculating a Percentage Increase Over Time from a Growth Model

Daily percentage growth would simply be the growth increment divided by the total increment for the day (day ‘n’ total minus day ‘n-1’ total) divided by day ‘n’ total.

The annual percentage would be worked out the same way, the total at the year-end, minus the total at the previous year-end, divided by the year-end total. The resultant fraction is of course multiplied by 100 to provide percent.

A formulaic way of presenting this is is as follows:

Current total = X

Previous total = Y

Percentage growth = (X-Y)/X x100

Percentage growth on a group would simply be the sum of the group’s growth applied in the same formula. There is no need to calculate an average since both lines would cancel themselves out.

An average growth rate would simply be a larger number increment converted to a smaller one. For example, taking the annual rate and dividing it by 365 provides an average daily rate, or taking the overall change over a number of days and dividing it by the number of days.

The percentage increase can also be called the rate of increase.

### Growth as a Percentage of Input

Another useful growth percentage for data analysis will be growth as a percentage of another factor. It’s important when considering another variable that apples are compared with apples.

If working out growth versus input as a percentage, then input and growth needless to say both need to be calculated with respect to the same time parameter, eg annual figures.

If a company spends 5000$ to grow their sales from 100,000 to 110,000, then effectively we can look at this two ways. The growth could be considered 200% of the marketing budget, or a 10% growth in overall sales figures.

### Calculating Individual Growth Versus Overall Growth

Percentages may also be represented in terms of the breakdown of components of growth versus overall growth. Total growth figures versus growth of an individual parameter. This type of parameter is most easily projected as a pie chart since the overall figures will add up to 100%.

This is a simple fraction, that is the number of the individual increase divided by the total increase, again of course, multiplied by 100 converts the fraction into a percent.

X = individual increase

Y = sum of all increases

% of X as a whole increase = X/Y x 100

### Errors in Representing Percentage Growth

A common sales technique is to indicate huge growth figures, eg 200% growth, then omit a time parameter, as 200% over a year or over 10 years tells a different story.

Another common error in representing growth is basing growth on an incorrect sum, 300% ROI (return on investment) on a project, where actual monetary growth is only 10% after expenses, so the gross return is provided not net return, little use to an investor.

### Reducing Models to Average Percentages

A model may be linear, but often it’s non-linear. To reduce a non-linear model to a linear model, a simple way is to consider two-point variables. That is taking two points on a curve of average representation, and connecting them to reduce the curve to a straight line.

The gradient of any straight line represents growth rate, which itself is a percentage. In this way, a complex mathematical model may be approximated by a percentage increase. In the reverse of the above percentage increase calculation, the previous sum (previous day or year) multiplied by the rate, equals the new modeled amount. The linear rate is, therefore, average increase over time.

### Graphical representation of Percentage Growth

When projecting growth modeling data as a percentage it is important to indicate what type of percentage is being displayed. Labeling of graphs is very important for correct data representation.

The type of graph used will depend on the type of data.

A bar graph is useful when considering a range of static growth rates, for example, the growth of population in cities, or the rate of increase in employee productivity in different companies.

A pie chart as discussed is the best method if the data being discussed is a fraction of a whole, for example, the growth of employees in each department as a percentage of overall employment growth across the company.

For any display of percentage growth versus time, a line graph is always best, since one axis, usually the horizontal one needs to show time.

### Data Analysis from Models to Percentages

It’s clear from the few simple examples above, that once data is created from mathematical modeling, it can be used to create valuable information for data analysis.