What Is Standard Deviation? How to Read and Assess It in SPSS

What Is Standard Deviation

You open your data file, run descriptive statistics, and see a column labelled Std. Deviation. This number is the standard deviation, usually abbreviated as SD. It shows how far the observations are dispersed from the mean.

When SD is small, the responses are relatively close to the Mean. When SD is large, the responses are more widely dispersed around the Mean. SD is always expressed in the same unit as the original variable. For example, if the variable is an evaluation score from 1 to 5, its SD is also expressed in score points on that scale.

For a sample with n observations, the sample standard deviation is commonly written as:

SD = √[Σ(xᵢ - x̄)² / (n - 1)]

Here, xᵢ is each observed value, x̄ is the sample mean, and n is the number of observations. Taking the square root of the variance brings SD back to the original unit. You can see a more detailed explanation of variance and the variance formula.

Standard deviation does not tell you whether a variable is good or bad, and it is not a score for questionnaire quality. You need to read it together with the Mean, Min, Max, sample size, and the purpose of the analysis.

The Meaning of Standard Deviation in Quantitative Research

In a thesis, SD first helps you describe how dispersed the data are. For example, the Mean of SAT1 is 3.80 and the SD is 0.62. This indicates a fairly high average response, while the responses are not all concentrated at exactly one value.

SD also helps you see differences between variables. Two variables may both have a Mean of 3.80, while one has an SD of 0.30 and the other has an SD of 1.10. The second variable is more dispersed, which means that respondents' views differ more clearly.

However, SD does not by itself prove that the data have a problem. A large SD may appear because the sample contains several groups of people with different characteristics. A very small SD may occur because respondents selected almost the same level, the questionnaire was too easy, the sample was too homogeneous, or respondents followed a repeated response pattern.

You commonly use SD in the following four situations:

• Describing the characteristics of items in Chapter 4.
• Comparing dispersion between variables measured on the same scale.
• Conducting a preliminary data check before running regression, EFA, or PLS-SEM.
• Interpreting respondents' level of agreement alongside the Mean.

For a nominal variable such as gender or field group, SD is usually not the main statistic to interpret. For a Likert variable, SD is commonly reported, but you still need to present how the scale was coded and the number of valid observations.

What Standard Deviation Is Acceptable

The question of what standard deviation is good does not have one general threshold that applies to every dataset. SD depends on the measurement range, coding method, sample distribution, and the content of the variable. Therefore, you should not remove a variable only because its SD is high or retain one only because its SD is low.

The table below shows how to read SD in common contexts. Thresholds with a source should be used only within the scope addressed by that source.

For a Likert scale from 1 to 5, an SD of 0.3, 0.7, or 1.1 can all appear in real data. The appropriate interpretation also depends on the Mean. An SD of 0.90 around a Mean of 3.00 indicates a different response pattern from an SD of 0.90 around a Mean of 4.40, even though the absolute dispersion is the same.

You also need to distinguish acceptable according to the objective. If you are describing the data, SD only needs to be reported accurately. If you are checking the conditions of a model, you must examine that model's relevant assumptions, such as outliers, multicollinearity, or residuals. There is no valid rule stating that every SD must be smaller than one particular number.

How to Read Standard Deviation in the Output

In SPSS, you can run Analyze > Descriptive Statistics > Descriptives. Move the variables you want to describe into Variable(s), select Options, tick Mean, Std. deviation, Minimum, and Maximum, then click Continue and OK.

Another option is Analyze > Descriptive Statistics > Explore. This command is more useful when you want to see additional frequency tables, boxplots, and checks for unusual observations. If you only need a short descriptive table for Chapter 4, Descriptives is usually sufficient.

Illustrative output

The table below models the structure of the SPSS Descriptive Statistics table. This is illustrative output, not the result of a real study.

Suppose the four rows are SAT1, SAT2, SAT3, and SAT4, respectively. For SAT1, the Mean is 3.82 and the SD is 0.71. You can write that the average evaluation of SAT1 is 3.82, with a dispersion of 0.71 points around the mean.

SAT4 has an SD of 1.02, which is larger than the other three variables. This is a reason to check the frequency table, boxplot, and original data. The result does not automatically mean that SAT4 is wrong. The item may describe an aspect on which respondents have more differentiated views.

When reading the output, check the N column first. If one variable has a substantially lower N than the others, the data may be missing or the item may not have been answered completely. Next, check whether Minimum and Maximum fall within the expected coding range. For a scale from 1 to 5, a value of 6 or 0 needs to be checked immediately.

You can also refer to the variance formula to understand why SD has a direct relationship with variance. If the Mean and SD are being influenced by a few extreme observations, check for outliers instead of manually changing the data.

How to write this in your thesis

You can adapt the following sentence to your output: “Descriptive statistics show that the variable [VARIABLE CODE] has a mean of [MEAN] and a standard deviation of [SD], based on [N] valid observations. The minimum and maximum values are [MIN] and [MAX], respectively, indicating that the data fall within the expected coding range of the [SCALE NAME] scale.”

If the SD is higher than the other variables, write cautiously: “The variable [VARIABLE CODE] has a relatively higher standard deviation than the variables in the same group. The study continued to check the distribution and unusual observations before deciding how to handle the data.”

What to Do When Standard Deviation Is Not Acceptable

First, identify the criterion behind the phrase not acceptable. If the only reason is that SD is large, stop at the checking stage and do not delete the variable yet. If the variable contains codes outside the expected range, an unusual N, or invalid values, those are the signs that require data handling.

Check coding and missing data

Open Analyze > Descriptive Statistics > Frequencies, move the variable into the list, and review the values that appear. Check codes such as 0, 99, 999, or blank cells. A code representing no response must be declared as missing rather than left for SPSS to treat as a valid score.

Check reverse-coded variables

If the questionnaire contains reverse-coded items, you need to recode them before calculating the scale score. For a scale from 1 to 5, the usual formula is that the new value equals 6 minus the old value. After recoding, run the descriptive statistics again and record which items were reverse-coded in the syntax or processing log.

Check outliers and unusual responses

Use the boxplot in Analyze > Descriptive Statistics > Explore to examine extreme scores. Compare them with the original file and the sampling criteria. You should remove an observation only when there is a clear basis, such as a data-entry error, failure to meet the screening conditions, or violation of the data criteria stated in the methods section.

Rerun the analysis with a controlled process

After each change, save a new version of the data and record the number of observations before and after processing. Do not delete several rows in succession simply to make SD look better. The committee may ask why a group of respondents was removed, and you need to answer with a criterion that was defined in advance.

If the data are valid and the large SD accurately reflects differences in the sample, keep it and interpret it. If the data are too homogeneous, a small SD is not a reason to create additional variation. Report the result accurately and consider the effect of the sample characteristics in the discussion section.

Distinguishing Standard Deviation from Variance and the Median

Standard deviation and variance both describe dispersion. Variance is the average of the squared deviations from the Mean, while SD is the square root of variance. Because variance uses squared units, SD is usually easier to read when writing a thesis.

For example, if SD is 0.71 points, the variance is approximately the square of 0.71. You should not interpret variance as though it were a number of points on the scale. The section on variance explains this difference in more detail.

The median, or Median, is the value in the middle after the data are ordered. The Median answers the question “What is the middle score in the sample?”, while SD answers “How are the scores dispersed from the Mean?” You can read more about the median when the data are skewed or contain extreme values.

Mean and SD are often reported together because they provide two complementary pieces of information. Mean shows the average level, while SD shows the dispersion. If you report only one of them, readers will have difficulty forming a basic picture of the data.

Common Mistakes

The first mistake is concluding that a smaller SD is always better. A small SD only shows that the data are concentrated. If everyone selected the same level because the questionnaire could not distinguish between different opinions, the information collected may be limited.

The second mistake is using one fixed SD threshold for every scale. SD for a scale from 1 to 5 cannot be interpreted in the same way as SD for income, age, or the number of purchases. Check the unit of measurement and the range of variation first.

The third mistake is seeing a large SD and then deleting the variable or the sample. This can easily produce results that have been adjusted to match expectations. Check missing data, coding, outliers, and collection conditions before making a decision.

The fourth mistake is confusing Std. Deviation with Std. Error. Standard error reflects the uncertainty of an estimate, while SD reflects the dispersion of observations. These two columns serve different purposes in SPSS output.

The final mistake is copying the entire output table into the thesis without interpretation. Select the necessary columns, use clear variable names, state the valid N, and explain the notable points. You can keep the complete output file in the appendix if your supervisor requires it.

Frequently asked questions

What standard deviation is acceptable?

There is no single number that applies to every variable. With Likert data, read SD together with Mean, Min, Max, N, and the distribution chart. If the data fall within the coding range, there are no unusual missing values, and SD accurately reflects the sample, you can report it instead of forcing it to meet a threshold.

Is a smaller standard deviation always better?

No. A small SD only shows that the responses are close to one another. This may fit an item with a high level of agreement, but it may also indicate that the sample is too homogeneous or that respondents followed a repeated response pattern.

Does a large standard deviation mean that the data are wrong?

You cannot conclude that from SD alone. Check values outside the expected range, missing data, reverse-coded variables, outliers, and the sampling process. If all values are valid, a large SD may reflect real differences between respondents.

How should I handle a standard deviation of 0?

An SD of 0 means that every observation for the variable has the same value. Check whether the variable was entered as a constant, the wrong sample was filtered, or the coding was incorrect. If the result is correct, the variable has no variation and usually provides little information for analyses that require differences between observations.

Do I need to check standard deviation before running regression?

You should run descriptive statistics to detect data errors before regression, but regression does not require every variable to have the same SD. Check the relevant assumptions for your analysis design, including unusual observations, linear relationships, multicollinearity, and residuals.

Open your SPSS file again, run Analyze > Descriptive Statistics > Descriptives, compare N, Minimum, Maximum, Mean, and Std. Deviation, then record your processing decisions in a copy of the data before writing Chapter 4. If you need to run the analysis on your own .sav or .csv file and explain the results, see the M4 data analysis module.