Experience is a great teacher. And in my experience, the beginning has always been tough.

As a BI consultant & trainer, I have worked with various people: from the frontline employees to CEOs. Our interactions gave me great insights into the multiple challenges they face.

I have put together a few pages from my experience and learning; covering Power BI, Excel, Power Query, Power Pivot, Tableau, data analytics & data visualization.

The purpose of the blog is to get you started.

I hope you’ll find them helpful.

Vivek

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## Statistics Simplified# 6: Geometric Mean

Statistics Simplified is the series to express statistics in layman terms.

Let us start with an example. Below is the year-over-year sales data, along with the %age change from the previous year:

What is the average %age change from the year 2014 to 2019?

If we calculate the arithmetic mean (aka average) of the % Change, we get 9.6%. It means, each year, there is a 9.6% change from the previous year.

If we apply a 9.6% year-over-year change, we get a different result than 3682 for the year 2019.

There is a difference of 14 units or 0.39%.

It signifies that arithmetic mean or simple average is incorrect in such scenarios.

## Geometric Mean for calculating an average of percentages

The geometric mean is applicable in such scenarios. The geometric mean of the above example is 9.5%.

When we apply 9.5% of change from the year 2014, we end up with 3,682 sales in 2019.

In Excel, we use the function GEOMEAN. Just like the function AVERAGE, it takes an array as an input. It requires one adjustment in the formula:

GEOMEAN (1+ <array>) - 1

Adding 1 to the range and then subtracting it offsets significant fluctuations and negative values.

Let us see one more example:

Here we see a significant difference between the average (arithmetic mean) and geometric mean (-3.2% vs. -9.9%).

Following is the difference when we apply this to validate the results:

The geometric mean is used in calculating the overall return% on stocks or investments over

time.

Also, see:

Mean vs. Median

Trim Mean

#vivran

## Statistics Simplified# 5: Trim Mean

Statistics Simplified is the series to express statistics in layman terms.

Photo by RF._.studio from Pexels

Got data points with special causes or outliers in your data set?

How to calculate the average in such cases?

A few common approaches are to either:

• exclude the record, or

• replace the extreme values with the median of the data set.

And there is another way: we use Trim Mean instead of a simple average.

## What is Trim Mean?

An average of the trimmed or “inner” data set.

### Which data points does it trim?

It excludes the data points from both ends.

## TRIMMEAN in Excel

Excel has function TRIMMEAN which takes two arguments:

• Array: The data range

• Percent: The percentage of data points to be excluded from the calculation. It takes values from 0 to 1. If we say percent = 0.2, then it will exclude 20% of the dataset from the calculation. So, if the data set contains 10 data points, then it will exclude 2 data points; 1 from the top and 1 from the bottom (as demonstrated in the image above).

Just like the median, it first sorts the data into an order and then excludes the extreme data points from both ends.

In the example below, TRIMMEAN excluded 2 & 100 from the calculation, as I have supplied 0.2 as a percent.

## Points to Remember

• TRIMMEAN function in Excel takes values greater than 0 and less than 1 in <percent>. Both 0 & 1 returns #NUM! error.

• TRIMMEAN excludes datapoints in the nearest multiples of 2. If the <percent> is .3 for the data set size of 10, it will remove 2 data points (one from the minimum and one from the maximum side).

Also, see:

Mean vs. Median

Geometric Mean

#vivran

## Statistics Simplified# 4: Mean vs. Median

Statistics Simplified is the series to express statistics in layman terms.

When it comes to understanding data, we prefer representing an entire data set using aggregations like count, sum, average, percentages. These aggregations summarize multiple data points into single points. These individual points typically represent the entire datasets, which makes comparisons and decision-making a more straightforward process.

Arguably, the average is the most popular aggregation when it comes to comparisons.

Reason: Average, or also known as the arithmetic mean, is easy to calculate.

## How to calculate the average?

We sum the entire data set and then divide it by the count.

Let us take the following sample dataset: 1, 2, 3, 4, 5

• Step 1: Calculate sum of all the numbers (1+2+3+4+5) = 15

• Step 2: Count all the numbers (1,2,3,4,5) = 5

• Step 3: Divide the output of Step 1 by Step 2 (15/5 = 3)

So, in simple words, we can say that the central data point of this dataset is 3. Or, most of the data points are around 3.

The fact that calculating average is an effortless process, and it is a representation of the entire dataset, makes average the most widely used aggregation.

Even Excel has two formula-less ways of calculating average:

### Pivot table

More on Value Field Settings

## So what is a Median?

Median is also a representation of the central tendency of the data point. Unlike average, the median is not a calculated value. It is a physical point in the dataset.

### Calculating the Median

We sort the data in an order (ascending or descending), and then the middlemost value becomes the median.

Case 1:

When the count of the data set is an odd number

Sample Data: 8, 6, 4, 10, 12

• Step 1: Arrange the data in an order -> 4, 6, 8, 10, 12

• Step 2: Find the middle number -> 4, 6, 8, 10, 12

Median = 8

Case 2:

When the count of data set is an even number

Sample Data: 8, 6, 4, 10, 12,2

• Step 1: Arrange the data in an order -> 2,4, 6, 8, 10, 12

• Step 2: Calculate the average of the middle two numbers: 2,4, 6, 8, 10, 12

Median = (6+8)/2 = 7

## Formulas in Excel

There are two simple formulas for average and median:

AVERAGE(<array>)

MEDIAN(<array>)

Vinci is a data analyst and lives in City A. One of his friends told him that data analysts in City B are getting higher salaries and recommends him to move to City B.

Vinci decided to analyze the wages for data analysts in two cities, A & B. He collected sample data for the two cities and calculated the average.

City A: \$ 121,012

City B: \$ 258,713

By just looking at this, City B appears to be a prospective location for business analysts as the average salary of City B is 114% higher than City A.

Then, he calculated median salaries for these cities:

City A: \$ 122,082

City B: \$ 121,511

The median salary of City B is, in fact, slightly lower than City A.

How is this possible? Why are the two characteristics of the central tendency of data telling two different stories?

To find out, Vinci decided to investigate the samples he had used for the analysis.

The salary for one of the samples is significantly higher than the rest of the group, resulting in changing the average value of the group salary.

Extreme values in the data set impacts the average. In such cases, the average can be a misleading representation of the dataset.

However, the median remains unaffected by such data points.

If we exclude Jen’s salary from Sample B and then the average wage of City B comes down to \$ 119,260. Now City B does not seem to be lucrative enough, in terms of salary.

He should collect more samples to support his decision to move to City B.

In a nutshell, while comparing performances, we should not wholly rely on averages and include other aggregations. Otherwise, we may end up deciding wrong!

Also see: Trim Mean

## Drop Me a Line, Let Me Know What You Think

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