The following (slightly modified) question was posted as a comment here, but I felt that the answer was too lengthy for the comments section.
Our questionnaire is composed of items with a 5 point scale, ranging from “1=strongly disagree” to “5=strongly agree”. For example, we are trying to find out if the respondents agree with [a topic]. The number of respondents who ‘strongly disagree’ are 2, those who ‘disagree’ are 9, those who ‘are undecided’ are 24, those who ‘agree’ are 18 and those who ‘strongly agree’ are 7. How do I interpret this data?
For such data, I suggest that you calculate the median and Inter-Quartile Range (IQR) of each item. The median (: the number found exactly in the middle of the distribution) is a measure of central tendency: very roughly speaking, it shows what the ‘average’ respondent might think, or the ‘likeliest’ response. The IQR is a measure of dispersion: it shows whether the responses are clustered together or scattered across the range of possible responses.
You can find some instructions on how to do calculate these metrics with SPSS in this page (the procedure is the same for both). If you only have access to Excel, here are links to a couple of videos demonstrating how to calculate the median and the IQR. For small datasets, such as yours, it is easy to calculate the median and IQR manually. In the next two sections, I shall show you how, using your example data.
Calculating the median
First, you arrange the numbers in an order from largest to smallest, like this:
1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3, 3,3, 3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5
To compute the median, you then delete one number from each end of the line, and repeat until you are left with just one number (or two that are the same). This ‘middle’ number is your median. If you are left with two different numbers in the end, the median is half-way between them. Using the data you provided, the median is 3, and I have marked it with red to make it stand out.
Calculating the IQR
The IQR is slightly more complicated, but not too hard. Your starting point will be the same arrangement of responses that we used above. When you divide this line into four equal parts, the ‘cut-off’ points are called quartiles. I have used red to indicate quartiles in your dataset.
[1,1,2,2,2,2,2,2,2,2,2,3,3,3, 3] [3,3,3,3,3,3,3,3,3,3,3,3,3,3, 3][3,3,3,3,3,4,4,4,4,4,4,4,4,4, 4] [4,4,4,4,4,4,4,4,5,5,5,5,5,5, 5]
The IQR is the difference between the first and third quartile. In your example, this is: Q3 – Q1 = 4 – 3 = 1.
A relatively small IQR, as was the case above, is an indication of consensus. By contrast, larger IQRs might suggest that opinion is polarised, i.e., that your respondents tend to hold strong opinions either for or against this topic.
Reporting the data
When your findings suggest consensus, your write-up should focus on describing the median (i.e., what most respondents seem to believe). One way to describe this is by writing something like: “most respondents indicated agreement with the idea that… (Mdn=4, IQR=0)”.
By contrast, when opinion is polarised, your write-up should emphasise the dissonance of opinion: the median is perhaps not so important. To help you understand this, consider a hypothetical case where half of your respondents hate a new textbook, and half love it. If you were to simply report that the respondents are, on average, undecided, that would be a statistical distortion of the data. Here’s a possible way to report the data more accurately: “Opinion seems to be divided with regard to… . Many respondents (N=28, 47%) expressed strong disagreement or disagreement, but a roughly equal number (N=26, 43%) indicated that they agreed or strongly agreed (Mdn=3, IQR=3).“
A final caveat
One last thing: I would caution you against placing too much faith on findings that were generated from a single Likert-type item. If at all possible, I’d try to cluster similar items together and compare / merge their results. If the findings are broadly consistent, that gives us confidence in them. If they are not, it might mean that one of the items did not function properly (e.g., respondents may have been confused by the wording), and you may have to discard it from the dataset.