Is it appropriate to use the mean and standard deviation when analyzing likert-scale data. I can't seem to get a solid answer to this question.
There is a lot argument going on regarding the Likert scale. As a rule of thumb, no. Single Likert variables are ordinal in nature, and as such do not uphold the interval restriction. Such survey questions that use a classical 5-point Likert scale:
Strongly Disagree | Disagree | Neutral | Agree | Strongly Agree I love long walks on the beach 1 2 3 4 5
Can scarcely be thought of as interval because respondents are unlikely to perceive the difference in categories as exactly equal (meaning that they are not equidistant).
On the other hand, in many cases in which several Likert questions are using the same scale in order to measure some underlying hidden trait, and then summed together, the result can be treated as interval. For (a very silly) example:
1. I love long walks on the beach 2. I love candle-light dinners 3. I love picnics during sunset 4. I love to lay on the grass and view the clouds ---- MEASURE SAPPY ROMANTIC TRAIT ----
It really depends on field and build of your data. See Andrew Messing's answer to a similar question on (gasp) ResearchGate. It has attached papers for different views and ways of dealing with Likert scaled data.