# Interpreting & Calculating Seasonal Indices

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• 0:03 Seasonal Indices
• 1:07 Calculating Seasonal Indices
• 2:09 Deseasonalizing Data
• 4:46 Lesson Summary

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Lesson Transcript
Instructor: Michael Eckert

Michael has a Bachelor's in Environmental Chemistry and Integrative Science. He has extensive experience in working with college academic support services as an instructor of mathematics, physics, chemistry and biology.

Seasonal indices can be used to deseasonalize and, thereby, smooth time plot data. That means seasonal fluctuations or patterns can be removed from the data, and forecasts can be made with regard to future data values.

## Seasonal Indices

Let's suppose that a fictional company sells widgets. This company recorded the number of sales of these widgets on a quarterly basis through two years, or eight times, which you can see in the table:

What will be the company's projected sales in quarter 9 (the first quarter of 2018) or quarter 10 (the second quarter of 2018)?

This is where we can implement seasonal indices to deseasonalize and, thereby, smooth data to allow for forecasting of trends. A seasonal index is a measure of how a particular season through some cycle compares with the average season of that cycle. By deseasonalizing data, we're removing seasonal fluctuations, or patterns in the data, to predict or approximate future data values.

Our fictional company wishes to project sales of widgets into 2018. Let's help them do this using:

• Seasonal indices
• Forecasting or trending
• Deseasonalized linear regression (remember that linear regression involves determining a straightforward relationship between an independent and dependent variable)

## Calculating Seasonal Indices

Before we begin, let's slightly reformat the table given our example to represent the number of sales in millions of widgets over eight quarters through 2016 and 2017. To avoid confusion, note that this table contains the same data as the prior table; it's just represented differently.

Furthermore, let's make a time-plot of that data:

We can use the time plot to make a visual note of the general shape and behavior of our sales through time.

To calculate seasonal indices, we first take the yearly average, or mean, of the quarterly sales, which you can see on the table:

Secondly, we divide each quarterly sales figure by its respective yearly mean, which gives us the following indices in the table:

Note how these index values rise and fall with their respective sales values. We then take the mean of these indices for each quarter to get our seasonal (or quarterly) index values:

Note how the index values at the bottom add up to 4, or the number of quarters. Also notice how the index values rise and fall with their respective quarterly sales.

## Deseasonalizing Data

We can use these seasonal (or quarterly) indices to deseasonalize and, thereby, smooth our sales data over the eight quarters. As shown, we divide each original sales figure by its respective quarterly index:

If we were to plot this deseasonalized sales data through eight quarters and superimpose it onto the original time plot for sales, it would look like this graph:

Note in this graph how this deseasonalized time plot could very well be helpful in forecasting future trends, as sharp seasonal peaks and troughs are smoothed, providing more basic visual aids for trending.

For instance, if we were to draw a straight trend line (by eye) through our deseasonalized sales data, we might see the following, noting that our trend line is shown here with a dotted line:

We also might use this line to visually predict upcoming sales for quarters in 2018.

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