Median Formula and How to Read the Results in SPSS

What is the median formula

The median is the value at the middle position when you arrange observations in ascending or descending order. Half of the observations are lower than or equal to the median, and the other half are higher than or equal to it. For this reason, the median is often used to describe the central position of data when the dataset contains extremely large or small values or is skewed.

The median formula depends on the number of observations, n:

• If n is odd, the median is the observation at position (n + 1) / 2 after the data has been sorted.
• If n is even, the median is the arithmetic mean of the two observations at positions n / 2 and n / 2 + 1.

For example, the sequence 3, 5, 7, 8, 12 has 5 observations. The median position is (5 + 1) / 2 = 3, so the median is 7. The sequence 3, 5, 7, 8, 12, 20 has 6 observations. The two middle positions are positions 3 and 4, so the median is (7 + 8) / 2 = 7,5.

You need to sort the data before applying the formula. If you take the first two values or the two middle values from an unsorted dataset, the result will be wrong. In SPSS, the software sorts and calculates the result automatically, but you still need to understand the logic so you can check the output.

The meaning of the median in quantitative research

In a quantitative thesis, the median helps you answer this question: at what level is a typical observation located? This statistic is particularly useful when the data is not symmetrically distributed. For example, the income of 100 people may be concentrated at a few million Vietnamese dong, while a small number of people have very high incomes. In that case, the median often represents the typical group better than the mean.

For a Likert scale, you can use the median to describe the response tendency, especially when you want to present additional information about the distribution. However, the appropriate reporting approach depends on your research design and your supervisor's requirements. Many theses report Mean, Median, Standard Deviation, Minimum, and Maximum together in the descriptive statistics table.

The median also helps you identify the difference between the central value and the mean. If the Mean is clearly larger than the Median, the data may be pulled toward larger values. If the Mean is smaller than the Median, the data may be pulled toward smaller values. You should also examine charts, Minimum, Maximum, and outliers instead of drawing a conclusion from one pair of numbers alone.

The standard deviation shows the degree of dispersion around the mean, while the variance is the square of the standard deviation. You can read a detailed explanation in standard deviation and variance. When you need to check whether an unusually different value is pulling the Mean away from the Median, also examine the outlier.

In practice, the median is commonly used for three decisions. First, it describes the typical level of a variable. Second, it helps identify skewed data or unusual values. Third, it helps you choose an appropriate way to present the Mean and Median. It is not a criterion for deciding whether a scale passes or fails, and it does not replace Cronbach's Alpha, EFA, regression, or PLS-SEM.

What median value is acceptable

The median does not have a universal threshold for deciding whether it passes or fails. You must read the median according to the scale and the meaning of the variable. For example, a median of 4 on a 1 to 5 Likert scale may indicate an agreement tendency, while a median of 4 for a variable measuring the number of purchases has a completely different meaning.

For a quantitative variable such as age, income, or years of experience, you cannot say that the Median must be higher than a fixed number. For a Likert variable, you can describe the median as low, neutral, or high based on the points of the scale you designed. This is a descriptive interpretation, not a statistical test.

If you need to interpret variance and standard deviation, do not assign the median a threshold that belongs to another statistic. The variance and standard deviation formulas describe dispersion, while the median describes central position. You can also consult variance formula when writing the methods or descriptive statistics section.

You should also distinguish thresholds such as Cronbach's Alpha from 0.7 up according to (Nunnally, 1978), KMO from 0.5 up according to (Kaiser, 1974), and factor loading from 0.5 up according to (Hair et al., 2010), because these apply to different analyses. Do not use these thresholds to assess the median.

How to read the median in SPSS output

You can calculate the median in SPSS in two ways. The first gives you a quick descriptive statistics table. Open the data file and select Analyze > Descriptive Statistics > Frequencies. Move the variable you need to inspect into Variable(s), select Statistics, check Median, Mean, Std. deviation, Minimum, and Maximum, then select Continue and OK.

The second method uses Analyze > Descriptive Statistics > Explore. Move the variable into Dependent List, open Statistics and keep Descriptives, then open Plots if you want to select Histogram or Boxplot. Select Continue and OK. This method is useful when you want to see the median together with dispersion and signs of an outlier.

The table below is illustrative output, not the result of a real study. The column names follow the way SPSS commonly displays the Descriptives table in the Explore procedure.

In the illustrative table, the Median is 4.00, meaning that the middle value of the variable is at level 4 on the scale. The Mean is 3.62, lower than the Median, which suggests that some lower-level observations may be pulling the mean down. This is only an initial observation. You need to check the chart and frequency table before saying that the data is skewed.

Std. Deviation is 0.713 and Variance is 0.508, giving two pieces of information about dispersion. Because the variance is the square of the standard deviation, 0.713² is approximately 0.508. Do not use Variance as a substitute for the Median, and do not use the Median to describe dispersion.

If you run Analyze > Descriptive Statistics > Frequencies, the Statistics table may display the columns N, Minimum, Maximum, Mean, Std. Deviation, and Median, depending on your selections. Check the exact variable name, the number of valid observations, and the number of missing values. If SPSS calculates different variables using different numbers of observations, state clearly how you handled missing values in the thesis.

What to do when the median does not meet expectations

Because the Median has no universal passing threshold, the phrase “the median does not meet expectations” usually signals that you are using the wrong evaluation method. First, check the scale and the meaning of the variable. A Median of 2 is not a software error if respondents genuinely tend to give low ratings.

The next step is to check the input data. Confirm that the variable was coded correctly, that the Likert levels fall within the expected range, and that no row contains a value such as 55 instead of 5. Select Analyze > Descriptive Statistics > Frequencies to view the frequency table. Any value outside the designed range should be checked against the original questionnaire or the data collection file.

Then inspect the Histogram and Boxplot in Analyze > Descriptive Statistics > Explore. If there is an outlier, do not delete it immediately just to make the Median or Mean look better. Check the original record, determine whether it is a data-entry error or a valid response, and record the reason if you decide to remove the row.

If the distribution is skewed but the data is valid, you can report both the Mean and Median, together with the standard deviation or Interquartile Range. This is easier to defend than changing the data. Only when the analysis objective requires a specific assumption should you choose a test that matches the distribution and research design.

How to write this in your thesis

You can write: “The variable [variable name] has a Median = [value], indicating that the typical response in the sample is concentrated at [interpretation level]. Mean = [value] and Std. Deviation = [value] are reported as additional information to describe the central position and dispersion of the data.” Replace every part in square brackets with the actual values from your file.

Distinguishing the median from the mean, variance, and standard deviation

The median and mean both describe central position, but their formulas are different. The mean formula is the sum of all observations divided by the number of observations: Mean = (x1 + x2 + ... + xn) / n. The Mean uses every value, so it is easily affected by an outlier. The Median depends only on the middle position after sorting, so it is usually more stable in the presence of extreme values.

For example, the sequence 2, 3, 3, 4, 20 has a Median of 3, while the Mean is 6,4. The value 20 pulls the Mean upward considerably, while the Median continues to represent the central group of observations. If you look only at the Mean, you may misunderstand the typical level of the sample.

Variance and standard deviation answer a different question: how far are the observations from the mean? Variance has squared units, while standard deviation has the same unit as the original variable and is therefore usually easier to interpret. When searching for the “variance standard deviation formula,” first decide whether you need to measure central position or dispersion.

You can read more about the median if you want to compare how the middle position is identified with the Mean across different types of data. When writing Chapter 4, present each statistic according to the question it answers. Avoid calling the standard deviation “the deviation of the median.”

Common errors when calculating the median

The first error is forgetting to sort the number sequence. With an odd number of observations, you will choose the wrong middle position if the data remains in its original entry order. With an even number of observations, a common error is to take only one of the two middle values instead of calculating their arithmetic mean.

The second error is confusing the Median with the Mode. The Mode is the value that appears most often, while the Median is the value at the middle position. A sequence can have multiple Modes, but the Median is determined by the position after sorting.

The third error is concluding that “a higher Median is always better” without checking the coding direction of the variable. If the variable measures the level of complaints, a high score may indicate a poor experience. Read the label for each level in the questionnaire before interpreting the result.

The fourth error is deleting an outlier simply because the Mean and Median are different. This difference may be a real feature of the data. Check entry errors, the response source, the Histogram, the Boxplot, and the methodological rationale before deciding what to do.

The final error is placing the Median in the reliability analysis as though it were a scale assessment statistic. Cronbach's Alpha and corrected item-total correlation serve that purpose. According to (Nunnally and Bernstein, 1994), a corrected item-total correlation from 0.3 up is a commonly used threshold, but it has no connection with the value of the Median.

Frequently asked questions

What is the median formula when there is an even number of observations?

Sort the data, take the two observations at positions n / 2 and n / 2 + 1, and then calculate the arithmetic mean of those two values. For example, the sequence 4, 6, 9, 11 has a Median of (6 + 9) / 2 = 7,5.

What median value is acceptable?

The Median has no universal passing threshold. You need to read it according to the scale, unit, and content of the variable. For a Likert scale from 1 to 5, a Median of 4 is often described as a high evaluation tendency, but this is a descriptive interpretation rather than a model acceptance criterion.

Where can I calculate the median in SPSS?

Select Analyze > Descriptive Statistics > Frequencies, click Statistics, check Median, and run the procedure. If you want to see a Histogram, Boxplot, and dispersion statistics as well, use Analyze > Descriptive Statistics > Explore.

Why are the Mean and Median different?

The Mean uses every value and can be pulled by an outlier. The Median is based on the middle position, so it is less sensitive to extreme values. A difference between the two statistics may suggest skewed data, but you need to inspect the chart and frequency table before drawing a conclusion.

Should I delete data if the Median is low?

Do not delete data simply because the Median is low. First check the coding direction, values outside the expected range, missing values, and unusual records. If the data is valid, report the result accurately and explain it according to the research context.

Open your SPSS file, run Analyze > Descriptive Statistics > Explore for the variables you need to report, compare the Median with the Mean, Std. Deviation, Histogram, and Boxplot, and record your decision for handling each unusual value. If you need to run the complete analysis process on your own .sav or .csv file, you can use M4 data analysis by DoThesis.