We're currently interpreting the results of our data gathering procedure, and these are the means and standard deviations of the scores we have gathered. I just wanted to know how do we interpret the standard deviations on this data set. I'm trying to learn more about it, but I can't quite easily grasp the concept when an SD can be considered as high or low. Thank you so much in advance to anyone who will assist us, we will use it as a guide in interpreting the rest of our tables!
Standard deviation is a measure of data dispersion; specifically, how far each data point, on average, falls from the mean.
What is considered a large or small standard deviation depends on what variable one is measuring and the range of possible values of that variable. Take Financial Accounting and Reporting in the table above. Assuming 83.02 is a mean rating score (rather than a sum), ratings ranging from 79.8 to 86.24 fall within 1 standard deviation of the mean.
If you square the standard deviation you obtain the variance of the set of observations. So, 3.22^2 = 10.3684. Thus, all raw ratings collectively spread 10.3684 points from the mean. Again, whether that is (practically-speaking) a large amount of variance or not I couldn't tell you.
Hello Arielle,
The answer to whether a given SD value is "high," "low," or "moderate" depends on the nature of the variable being measured and the population from which the cases have come. In other words, you can compare the variation on a given measure or score from samples over time to see whether the results suggested stable variation, or changes (increases or decreases) in score variation. Alternatively, you can compare the relative variation of separate batches, measured using the same scale.
What you could say, descriptively, from your data table is:
1. Relatively, taxation ratings are the most variable/spread, whereas auditing are the least variable/spread. So, there were more, and generally larger, differences in the set of taxation rating scores than for all others. As well, auditing rating scores were more homogeneous than all others.
2. If ratings were normally distributed, you'd expect to find that about 67% of cases had Advanced Financial Accounting/Reporting ratings somewhere between 79.06 and 85.16. (e.g., 82.11 +/- 3.05)
3. For an unknown distribution shape, you could be confident that at least 75% of cases had Management Advisory Services ratings somewhere between 71.04 and 86.32 (e.g., 78.68 +/- 2*3.82, via Chebychev's inequality)
4. Without knowing your sample size, one can't make any statement as to whether the relative variations for any specific set or subset of your results were significantly different (e.g, the values of 3.22 for SD vs. 3.05).
Good luck with your work.
In statistics, the standard deviation is a measure of the amount of variation or dispersion in a set of data. A higher standard deviation indicates that the data values are more spread out from the mean, while a lower standard deviation suggests that the data values are more tightly clustered around the mean.
In your research data, the standard deviation can be used to provide insights into the variability of your data. Specifically, you can use the standard deviation to:
It is important to note that the interpretation of the standard deviation may depend on the context of your research question and the specific characteristics of your data. Therefore, it is recommended that you consult with a statistician or data analyst to ensure that you are correctly interpreting the standard deviation in your research data.
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