2 Replies Latest reply on Mar 5, 2013 2:26 PM by Stuart Ramsbottom

# Calculating the median of Likert scale data that assumes that the 5 point scale represents a continuous random variable

the median is calculated in a way that assumes that the 5 point scale represents a

continuous random variable rather than five discrete categories. So for example, all those who select a 4 (i.e.

agree) are assumed to be evenly distributed between 3.5 and 4.49. Similarly all those who select a 5 (i.e.

strongly agree) are assumed to be evenly distributed between 4.5 and 5.49. The median is then calculated from

these transformed responses. The following example shows the steps to calculating the median.

Category                          No. of respondents      Cumulative no. of respondents

1 – Strongly Disagree      0                                    0

2 – Disagree                    0                                    0

3 – Neutral                       1                                     1

4 – Agree                          22                                  23

5 – Strongly Agree           26                                    49

Total                               49

Step 1 – The middle point is calculated by dividing the total number of responses by 2. So 49/2 = 24.5.

Step 2 – The category in which this middle point falls is identified. In this case 24.5 falls in the ‘5 Strongly Agree’ category as there are 23 respondents up to category 4 (see the Cumulative no. of respondents column).

Step 3 – As there are 23 respondents up to category 4, the difference between the middle point (i.e. 24.5) and 23 is calculated. So 24.5‐23 = 1.5. This tells us how many ‘places’ away from the bottom of category 5 is the median.

Step 4 – The 26 respondents who answered with a ‘5 – strongly agree’ are then assumed to be evenly distributed between 4.5 and 5.49. We need to identify where ‘1.5 places’ into that range sits. As there are 26 respondents the fraction 1.5/26 is calculated (0.06). This is then added to 4.5 (the bottom of the range) to give a median of 4.56.

• ###### 1. Re: Calculating the median of Likert scale data that assumes that the 5 point scale represents a continuous random variable

Stuart,

I want to thank you for posing this problem.  It is very rare that I get to used my statistics education in my current role .  With that said, Look at the attached workbook.  I believe it solves exactly your problem.  Set 1 is the set of values you gave and Set 2 is a value I made up.

EDIT: I find this instance to be a fascinating use of Tableau and will create a blog post about it.  My blog is referenced in my signature.  Let me know if there's any way I can credit you.

Thanks,

Associate Consultant

Mariner, LLC

http://breaking-bi.blogspot.com

• ###### 2. Re: Calculating the median of Likert scale data that assumes that the 5 point scale represents a continuous random variable

Thank you so much.

That's brilliant.

Regards

Stuart