Measurement of Central Tendency featured image

Measurement of Central Tendency : With Formula and Excel Functions

It is often used when you want to find the central position of the data in a dataset. Mean. Mode and Median are using in the measurement of the central position for a set of data. Measurement of Central Tendencies may be affected by the outliers, you will know more in details here. If you already know the measurement of Central Tendency, then you can read measurement of Dispersion an up gradation of Measurement of Central Tendency.

In the measurement of Central Tendency, we measure data using mean, Mode and Median. Let’s know each of them in details.

Mean (Average)

It is also called as the calculated average of a dataset.  You can say it is the most frequent use measurement of central tendency. In addition, It uses in both continuous and discreet dataset.  It is the sum of all the values in a data set divided by the total number of values in a dataset. Mean can change if we add new or remove value. It can also be changed if we add the large value to the data. The formulae for calculating the mean in mathematics is:

Sample Mean formula
Sample Mean formula

How to calculate Mean in Excel?

In excel you can use the following function to find the mean or Average.

= AVERAGE(value1[value2, ...])

The Value2 is optional.  It will calculate the Mean of all the selected values in the dataset.

Mean of the Dataset
Mean

You can see in the above figure I am using the =Average(B2: B11) for calculating the mean of the values in Column B and it’s 90.7. If I will add a large value to the data then mean will also increase.

Where you can use Mean in Real Life?

Sports – Player Average Score.

Academics – Average Marks of the student.

Stock Markets – Moving Average, Exponential, Simple and Weighted Moving Average.

Median

You can say median as the middle value in a given dataset. Data values must be sorted for calculating the mean. If the values are random, then you have to first order it in ascending order to find the median. The formulae for the median is different in case of odd and even value. The formulas for the median is given below.

Cases:

Number of values is Odd

In this case, median is the value at the (n+1 )/2.

Number of values  is Even

Then the mean will be average of the values at (n/2) and (n+1)/2.

How to calculate the Median in Excel?

You can use the MEDIAN(value1[value2, …]) function for calculating the mean. The value2 is optional. For example, in the below figure I used the function =MEDIAN(B2: B11) for finding the median of the dataset.

Median of the data
Median

Where you can use Median in Real Life?

Economics: Household Income of a Country.

Academics: Student Placement Packages

Real Estate: Price of a House

Stock Market – Median Price to Earning Ratio, P/E.

Mode

It is the most frequent occurrence of a value in a dataset. On a Histogram, Mode is the highest bar in a bar chart or Histogram.

How to calculate the Mode in Excel?

You can easily calculate mode in the excel using the function = MODE(value1[value2, …]. The value2 is optional. Like in the below figure, I am using =MODE(B2: B11) and the Mode of the Data is 120. that is the most occurrences of the number.

Mode of the Data
Mode

Where you can use Mode in Real Life?

E-commerce- Mostly sale items

Stock Market – Price Level,( Finding the most occurrence of a Price of a stock market. )

When to use Mean, Median and Mode?

If you have a dataset and are confused where to use median, mode in data variable then consider the following table. Nominal, Ordinal, Interval and Ratio are all level of measurements.

Type of Variable Best measure of central tendency
Nominal Mode
Ordinal Median
Interval/Ratio (not skewed) Mean
Interval/Ratio (skewed) Median

 

Conclusion

Measurement of Central Tendency is mainly affected by the presence of outliers. And also it doesn’t tell the relationship between the central positions and the remaining data as compared to measurement of dispersion. In all the measurements you will mostly use Median and Mean in Statistics like for finding Standard Deviation, Hypothetical Testing e.t.c.  I hope you understood what is Measurement of Central Tendency and how to calculate mean mode and median. Also where to use all these in real life.

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