What is Mean?- Measures of Central Tendency

Let’s first understand what central tendency is –

As the word suggests, it is a single data point that represents a data set’s central point or the middle point. It represents a value in such a way that half of the data set is before that value and the other half is after that value (figuratively speaking). Measure of central tendency helps describe an entire data set with a single value. There are three types of measures of central tendency – Mean, Median and Mode. In this post, we will understand Mean.

What is Mean?

Simply, it is the average of all values in a data set. In mathematical terms, it is the sum of all data points in a data set divided by the total number of values in that data set. In statistics, you always calculate a sample mean and based on the sample mean you assume the population’s mean. Let’s understand this with the help of an example. Let’s suppose you run a contact center and would like to find out how many calls you receive on an average every day. You collect the data for 5 days (in real business scenarios, you would want to collect the data for many more days). The data you gather is as follows:

Day # of Calls
Day 1 2378
Day 2 2892
Day 3 2288
Day 4 2401
Day 5 2333

 

How to Calculate Mean (Average) Manually?

Step 1: Calculate the total number of calls in 5 days. The sum of this data set comes out to be 12292 calls in 5 days.

Step 2: Calculate the number of data points in the data set. In the example above; there are a total of 5 data points.

Step 3: Divide the total of the data set by the total number of data point. In this example, you will divide 12292 by 5. The result is 2458.4. Logically, you can’t get 0.4 calls and hence, you will round that number off to 2458 calls.

How is Mean Represented in Mathematical Terms?

Refer the image below:

How to Interpret Average?

The interpretation of the average (or mean) is “you receive 2458 calls in a day on an average”.

What is the main disadvantage of Mean?

The main disadvantage of mean is that it is very sensitive to extreme values. Even a single extreme value the skew the average a lot. In our example that we took above, let’s replace one of the values (say, day 3) to 7500 calls – that is for some reason, you receive a lot more calls on day 3 than usual. Can you calculate the average now? If you calculated it, you would have seen a jump of nearly 1100 calls in the average. By replacing 2288 calls by 7500 calls, you get an average of 3501 calls. That average is much higher than the actual data points on the rest of the days. Assume that you are trying to staff your call center based on the average number of calls (there is better staffing methods available). Each person has the capacity to receive 100 calls each day based on the average handling time of a call. Please reflect back on the previous statement. The capacity of 100 calls is based on “AVERAGE” handling time of a call. Do you see how averages can be useful? Coming back; if each person can handle 100 calls in a day, how many do you need based on our original data? Remember, the average was nearly 2400 calls. Simple division of 2400 by 100 gives you a number of 24. Hence, you need 24 employees to work in your contact center to take the average number of calls of 2400. Now, in the new data, the average is nearly 3500. Divide that by 100 and you get 35 employees. If you staff at 35 employees, is that profitable for your business? No.

Hence, you should take out extreme values; in statistics, they are called outliers before you calculate the average (or mean).

How to take out average in Microsoft Excel?

It is very simple to find out average in MS Excel. You can do so by enter the formula: “=average(data set).

Hope you found our first article on Statistics Basics useful. Come back for more tomorrow.

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