I noticed on the Internet and even on RG that many researchers escape the answer of this question, where they say it is not good or bad, but it is low and high. For low SDs, we know that the variance is small and the values are close to the mean, but for large ones, we see data dispersed around the mean.
Still, the question is how large and how low...? Still I did not get am answer?
There were some related questions that were previously asked on ResearchGate and the numerous answers provide some insight to your question: https://www.researchgate.net/post/Which-method-should-I-use-to-present-the-Mean-of-a-5-point-Likert-scale
https://www.researchgate.net/post/How_to_interpret_mean_and_standard_deviation_for_a_likert_type_survey
It doesn't matter what the SD is. What matters is the p value obtained in the analysis. If it is < 0.05, then you can do post hoc tests to compare means. Otherwise the analysis ends and you accept the null hypothesis that the results were obtained simply by chance :)
Andrew Paul McKenzie Pegman Rodney Duffett
I did not chec the links, but I made a research (some of it on RG0 and found the same answers (Like what Andrew mentioned). I ask a different question. I need to say that this is a small SD, and data is not disputed among subjects, while a large SD means data is disputed... Which means I need a threshold for a 5 point liket scale.
Example: a mean = 4.2, with SD =1.2
or a mean =3.4, with a SD = 0.79... what does that mean... which one has a low consensus or both are, or high consensus,,,
You compare those means using the original data file by Chi Square test and use the resulting p value to know if the means are significantly different (as I outlined above). The test takes the SD into account :)
I guess we teach our students to check both (Mean and SD) as we can have the same mean with different SDs. Which means that the SD calculations are not integrated into the Chi Square value, but can have both... I guess
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