Mean, Median and Mode are three basic ways of finding central tendencies in statistics, there are several other ways to find central tendencies in statistics however mean, mode, and median are the most common concepts in statistics.

These concepts are most important to learn before starting any statistical course.

In this section, we will learn about mean, mode, median and understand under what conditions they are most appropriate to use.

Mean

Mean or arithmetic means is the most popular way to find averages and one of the simplest ways to find central tendency. It can be used for both discrete as well as continuous data.

To find out the mean for data you have to simply add all the values that you have in your hand and then divide the sum of the values with the total number of values used.

Formula:            Mean= (x1 + x2 + x3 +……+xnn)/n

where x1, x2,…..xn are values and n is the number of values.

For example : 

                      We have the following numbers as the  data:

                        11,  3, 5, 8, 6, 20, 15, 4, 9, 7

                      Therefore, the sum = 11+3+5+8+6+20+15+4+9+7 =88

                               No. of values= 10

                       Therefore, Mean = 88/10 = 8.8

Mean minimizes the error in the prediction of any value in the data, so we can say that mean is the value that produces the lowest amount of errors.

1. Mean includes every value of the data as a part of calculation.
2. Mean is highly affected by the presence of few abnormally high or abnormally low values.

Median

The Median is the middle value in the data set arranged in the order of magnitude.

Median is observed by arranging the data values in numerical order of smaller to largest.

For example:

                      We have the following numbers as the  data:

                        11,  3, 5, 8, 6, 20, 15, 4, 9, 7,10

                       Therefore, the sorted list is:

                        3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 20.

                       Since we have 11 values and the value at 6th position is median:

                      Therefore 8 is the median.

If you have an even number of data values, find the two middle values, then add them and divide the sum by 2. The Result is the median number.

For Example:

                       We have the following numbers as the  data:

                        11,  2, 3, 5, 8, 6, 20, 4, 9, 7,10

                       Therefore, the sorted list is:

                        2, 3, 4, 5, 6, 8, 9, 10, 11, 20.

                     Since we have 10 values then the two middle values are: 7 & 8

                        Therefore, 6+8 = 15, 14/2 = 7

                      Median = 7

1. Median is not affected by very large and very long values
2. It is a time consuming process for large data sets.

Mode

Mode is nothing but the most frequent value in the data set.

A data set where no value occurs more than once has no mode. Also, it is possible to get more than one mode for a data set.

For example:

                      We have the following dataset:

                        3, 4, 5, 5, 2, 10, 6, 9, 5, 1

                       Therefore the mode for this data set is 5.

Since there is a possibility of having more than one mode or no mode at all, that means mode is not always representative of data.

These are the basic concepts that are necessary to learn for any statistical course, if you want to be a master in statistics you can come to TutorBin. TutorBin helps students with their homework, we provide video solutions to students for their better understanding of the students.

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Frequently Asked Questions :

1. How can you find the mean for a data set ?

The median for a data set can be found out by adding all the data values and then dividing the sum by the number of data items.

2. Under what conditions can we find the mode for a data set?

Mode is the preferred measure of central tendency for nominal scale( in some cases for ordinal scale).

3. What are the factors that affect the median of a dataset ?

Median primarily depends on the order of the data.

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