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When analyzing your survey, there are nearly infinite ways to look at your data. It may be helpful to think about different types of data in terms of how they can be measured to determine central tendencies of each.  Measures of central tendency (mode, median and mean) attempt to describe a group of data with a single point. In our last article, we reviewed Mode Measurement, now we’ll discuss Median Measurement.

Median Measurement: Data Types: Ordinal & Ratio

Median, another measure of central tendency, can be used for both ordinal and ratio data.  The median is the middle point in the data.  In order to calculate the median, each data point is ranked in order and then the middle point is determined.

Example question: Ordinal Data Collection

The median is the {(n+1) ÷2}th  , where “n” is the number of respondents for the question, or the number of data points.  This formula means, that after you have ordered the data points numerically, the {(n+1) ÷2}th point will be the median.

 

For a small dataset of 5 responses (L,S,XL,L,S):

Step 1: Order responses least to greatest

Step 2: Find the median point

Since there are 5 responses or data points, then {(5+1) ÷2}th is the point that is the median.

{(5+1) ÷2}th = 3

Median = the 3rd data point in the ordered series above.

Step 3: Determine the median point

The 3rd point  in the ordered data series above is L, therefor Large is the median shirt size for the dataset.

For larger datasets, Just like when determining mode, a frequency table is useful in visualizing the data. In fact, it’s possible to treat ordinal data just like nominal data and stop there.  In this case, you may report the mode, XS, as the most common shirt size. Median will describe the data in a way that takes into account it’s relative meaning within the dataset and provide a richer explanation.

Step 1: Order responses least to greatest

(This is done above in the frequency table)

Step 2: Find the median point

Since there are 399 responses or data points, then {(399+1) ÷2}th is the point that is the median.

{(399+1) ÷2}th = = 200

Step 3: Determine the median

Looking back at the frequency table, it can be seen that the 200th data point in the ordered series is a S.  In large datasets, adding cumulative sums to frequency tables can be helpful. The median (200th point) is after the XS because those are only points 1-86.  The 87th point in the ordered data is a S.  All of the data points between 87-220 will be S, then the 221st point will be M and so on.  There’s no need to go further, because we have found our median.

What if the median is between two points?  This can happen when you have an even number of respondents for a question. In that case, the average of those two items will be the median.  If the items are both S, then the average of those is S so report S as the median.  If the items, in this type of data are different, then report the range (ex. S-M).

Likert-Type Scales:

 There is much debate over whether scaled items, such as Likert-type scales, can be treated as interval or ratio data, or whether they are relegated to ordinal data analysis methods only.  By definition, in order to be considered interval or ratio data, the distance between each scale point must be the same. That means that the subjective difference between “somewhat unlikely” and “neither likely nor unlikely”, must be the same as the subjective distance between “extremely unlikely” and “somewhat unlikely”.  Both mode and median can be used to assess individual Liker-type questions.  However, if there is a need to compare multiple questions, calculating weighted means may tell you the likelihood of respondent behaviors (see below for details).

Now that we’ve covered Median Measurement, next week we will round out our data measurement series by reviewing Mean Measurement.

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Scott Hutchins

Technical Co-founder

Scott Hutchins
Scott Hutchins

Scott Hutchins

Technical Co-founder

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