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. Answer from David Morse on researchgate.net
Statistics By Jim
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Standard Deviation: Interpretations and Calculations - Statistics By Jim
September 24, 2025 - So, consider this example to be ... they both show 30 minutes. The difference in results illustrates the effects of the larger standard deviation for the same defined time period (≥ 30 minutes)....
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Standard Deviation Calculator
standarddeviationcalculator.io › blog › how-to-interpret-standard-deviation-results
How to Interpret Standard Deviation Results
The interpretation of standard deviation becomes much more relatable when applied to real-world scenarios. For instance, in finance, a high standard deviation of stock returns would imply higher volatility and, thus, a riskier investment. In research studies, a high standard deviation might reflect a larger spread of data, which could influence the study's reliability and validity. Understanding and interpreting standard deviation results is a skill that proves valuable across multiple disciplines, from finance to scientific research.
National Library of Medicine
nlm.nih.gov › oet › ed › stats › 02-900.html
Standard Deviation - Finding and Using Health Statistics - NIH
A standard deviation close to zero indicates that data points are very close to the mean, whereas a larger standard deviation indicates data points are spread further away from the mean.
Statistics LibreTexts
stats.libretexts.org › campus bookshelves › taft college › behavioral statistics 1e › unit 1: description › 3: descriptive statistics
3.7: Practice SD Formula and Interpretation - Statistics LibreTexts
October 1, 2025 - The standard deviation is always positive or zero. The standard deviation is small when the data are all concentrated close to the mean, exhibiting little variation or spread. Distributions with small standard deviations have a tall and narrow ...
Greenbook
greenbook.org › insights › research-methodologies › how-to-interpret-standard-deviation-and-standard-error-in-survey-research
How to Interpret Standard Deviation and Standard Error in Survey Research — Greenbook
Put another way, Standard Error is the Standard Deviation of the population mean. Think about this. If the SD of this distribution helps us to understand how far a sample mean is from the true population mean, then we can use this to understand how accurate any individual sample mean is in relation to the true mean. That is the essence of the Standard Error. In actuality we have only drawn a single sample from our population, but we can use this result to provide an estimate of the reliability of our observed sample mean.
Top answer 1 of 4
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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.
2 of 4
1
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.
Reddit
reddit.com › r/explainlikeimfive › eli5: someone please explain standard deviation to me.
r/explainlikeimfive on Reddit: ELI5: someone please explain Standard Deviation to me.
March 28, 2021 -
First of all, an example; mean age of the children in a test is 12.93, with a standard deviation of .76.
Now, maybe I am just over thinking this, but everything I Google gives me this big convoluted explanation of what standard deviation is without addressing the kiddy pool I'm standing in.
Edit: you guys have been fantastic! This has all helped tremendously, if I could hug you all I would.
Top answer 1 of 23
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I’ll give my shot at it: Let’s say you are 5 years old and your father is 30. The average between you two is 35/2 =17.5. Now let’s say your two cousins are 17 and 18. The average between them is also 17.5. As you can see, the average alone doesn’t tell you much about the actual numbers. Enter standard deviation. Your cousins have a 0.5 standard deviation while you and your father have 12.5. The standard deviation tells you how close are the values to the average. The lower the standard deviation, the less spread around are the values.
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My explanation might be rudimentary but the eli5 answer is: Mean of (0,1, 99,100) is 50 Mean of (50,50,50,50) is also 50 But you can probably see that for the first data, the mean of 50 would not be of as importance, unless we also add some information about how much do the actual data points 'deviate' from the mean. Standard deviation is intuitively the measure of how 'scattered' the actual data is about the mean value. So the first dataset would have a large SD (cuz all values are very far from 50) and the second dataset literally has 0 SD
LeanScape
leanscape.io › home › lean wiki › demystifying standard deviation: a beginner’s guide
Demystifying Standard Deviation: A Beginner's Guide - LeanScape
However, to keep the standard deviation within the same units, we must then apply the square root of the variance. Don’t get confused. We square the data values to turn the negatives into positives but to end up with the same unit size, we then square root the result to get the final standard deviation.
Published September 23, 2024
Centennial College
libraryguides.centennialcollege.ca › c.php
Describing Data using the Mean and Standard Deviation - Statistics - Library Guides at Centennial College
A large standard deviation indicates that the data points are far from the mean, and a small standard deviation indicates that they are clustered closely around the mean.
Statalist
statalist.org › forums › forum › general-stata-discussion › general › 1344076-how-to-use-standard-deviation-to-interpret-results
How to use standard deviation to interpret results? - Statalist
This usually arises in a context where the explanatory variable is entered into a regression model after it is standardized to a mean of zero and a standard deviation of 1. In that case, a 1 standard deviation increase in the explanatory variable is the same thing as a unit increase in the standardized version used in regression, and the effect on the outcome variable being reported is just the marginal effect or elasticity of that standardized explanatory variable. When the explanatory variable has no natural metric or scale this may be an appropriate way to present results.
LinkedIn
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How can you interpret standard deviation in research results?
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Wikipedia
en.wikipedia.org › wiki › Standard_deviation
Standard deviation - Wikipedia
5 days ago - Squaring the difference in each period and taking the average gives the overall variance of the return of the asset. The larger the variance, the greater risk the security carries. Finding the square root of this variance will give the standard ...
Lippincott Williams & Wilkins
journals.lww.com › crst › fulltext › 2022 › 05040 › do_you_have_a_standard_way_of_interpreting_the.22.aspx
Do you have a standard way of interpreting the standard... : Cancer Research, Statistics, and Treatment
Shapes of two populations with datapoints that have a large spread (high standard deviation) and a lesser spread (low standard deviation) In statistics, the phenomenon of probability distribution distributes the values of a variable as per their corresponding probabilities. This is also called the Gaussian distribution, after the famous mathematician Friedrich Gauss. When repeated measurements are taken, such as in imprecision studies, the resulting data are often normally distributed. If we were to divide the dataset derived from these normally distributed data points into quartiles, or four equal sections, the quartile cut-off value is 0.68 standard deviations above and below the mean.
The BMJ
bmj.com › about-bmj › resources-readers › publications › statistics-square-one › 2-mean-and-standard-deviation
2. Mean and standard deviation
February 9, 2021 - For example, a lecture might be rated as 1 (poor) to 5 (excellent). The usual statistic for summarising the result would be the mean. In the situation where there is a small group at one extreme of a distribution (for example, annual income) then the median will be more “representative” of the distribution. My data must have values greater than zero and yet the mean and standard deviation are about the same size.