What Is the Median? How to Calculate and Interpret It

What Is the Median

The median is the value in the middle of a set of numbers after the observations have been arranged in ascending or descending order. If 50% of the observations are less than or equal to the median and 50% are greater than or equal to it, you are looking at the median of that variable.

For example, the set of scores 4, 6, 7, 8, 15 contains 5 observations. The value in the middle is 7, so the median is 7. For a set with an even number of observations, such as 4, 6, 8, 15, the median is the mean of the two middle values: (6 + 8) / 2 = 7.

The formulas can be written as follows:

• If the number of observations n is odd, the median is the value at position (n + 1) / 2 after sorting.
• If n is even, the median is the arithmetic mean of the values at positions n / 2 and n / 2 + 1.

In quantitative research, you calculate the median from a numerical variable or an ordinal variable that can be ordered. You can view the median alongside the mean, standard deviation, and range in the descriptive statistics section. When you need to read more about dispersion, see standard deviation and variance.

The Meaning of the Median in Quantitative Research

The median answers this question: what is the value at the center of the sample. It helps you describe a survey sample without allowing a few unusually large or small observations to change the central result substantially.

Suppose you survey the income of 7 people and obtain the values 8, 9, 10, 11, 12, 13, 100 million VND. The median is 11 million VND. The arithmetic mean is approximately 23.3 million VND because the value 100 pulls it upward. If your goal is to describe the typical income of the group, the median often gives a more understandable picture of the central position.

This is particularly useful when the data are right-skewed, left-skewed, or contain an outlier. You can also read about outliers in data to check why a few extreme values change the mean.

In a thesis, the median is commonly used to:

• describe demographic data such as age, income, and years of experience;
• describe the time, cost, or number of times a behavior occurs;
• supplement the mean when the data distribution is not symmetric;
• divide the sample into low and high groups according to the central value;
• support reporting of the 25th percentile, median, and 75th percentile.

The median does not tell you whether the data are widely or narrowly dispersed. Two groups with the same median of 4 can still have very different standard deviations and ranges. Therefore, you should not look only at the median and conclude that the data are stable. Read it alongside the standard deviation, minimum, maximum, and percentiles.

With a Likert variable, interpretation requires care. A 1 to 5 scale can report the median to describe the response tendency, but when you construct a composite variable and run later analyses, you must follow the method presented in the methodology chapter. The median does not automatically replace the mean in every model.

What Median Value Is Acceptable

The question "what median value is good" often appears when you see a number in a statistics table. There is no general threshold that applies to the median in every topic. Whether a value is acceptable depends on the variable being measured, its unit, the permitted range, and the research hypothesis.

For example, a median of 4 on a 1 to 5 Likert scale may indicate a positive evaluation tendency. A median of 4 years for an age variable means something entirely different. Read the median in the context of the variable, rather than applying the rule that a higher value is always better to every dataset.

The table below helps you decide how to interpret the result. The thresholds in the table are rules or sources for the relevant indicators, not mandatory thresholds for deciding that a median value is acceptable.

If you are asking what median is good for a 1 to 5 questionnaire, first identify the midpoint, which is 3. A median above 3 indicates that at least half of the observations are above the midpoint, but the specific conclusion still depends on the frequency at each response level. A median of 4 does not tell you how many people selected 5 unless you also examine the frequency table.

How to Read the Median in the Output

In SPSS, you can run descriptive statistics at Analyze > Descriptive Statistics > Frequencies. Move the variable you want to examine to the Variable(s) box, select Statistics, check Median, then select Continue and OK. If you also want the mean, standard deviation, minimum, and maximum, check the corresponding statistics in the same window.

The Statistics table usually displays the number of valid observations, the number of missing observations, the mean, the median, and other descriptive indicators. Column names can vary depending on the version or the options you select, but the reading logic remains the same.

Illustrative output

The following is illustrative output, not the result of a real study. Suppose you have a variable called SAT_MEAN, which is the mean score for a satisfaction scale from 1 to 5.

The reading is as follows: there are 180 valid observations and 3 missing observations. A median of 3.80 means that half of the observations have values no greater than 3.80 and half have values no lower than 3.80. The mean of 3.74 is slightly lower than the median, so the data may be slightly skewed toward lower values, but you need to inspect the chart or percentiles before confirming the shape of the distribution.

If the Mean is much higher than the Median, check whether the data contain some large values. If the Median is higher than the Mean, some small values may be pulling the mean downward. This is only an initial indication, not a test of skewness.

You can also use Analyze > Descriptive Statistics > Explore. Move the variable to Dependent List, select Statistics to view descriptive indicators, and select Plots if you need a boxplot. A boxplot helps identify observations that are far from most of the data. When checking data before analysis, record the number of missing observations, how they were handled, and the reason for retaining or removing unusual values.

How to write this in your thesis

You can adapt the wording as follows: “The descriptive statistics results show that the variable [VARIABLE NAME] has a median of [VALUE], with 50% of observations having values no greater than [VALUE] and 50% having values no lower than [VALUE]. The median was considered together with the mean, standard deviation, and range to provide a complete description of the data.”

What to Do When the Median Is Not Acceptable

The median does not have an acceptable or unacceptable status in the same way as Cronbach's Alpha, KMO, or a p-value. If the median is lower than expected, do not delete data simply to raise the number. Work through the following checks in order.

Check the scale and coding

Review the value labels, measurement range, and reverse-coded variables. A variable that should have been coded from 1 to 5 but was entered from 1 to 7 will be difficult to interpret through its median. For a reverse-coded variable, check the coding formula before calculating the composite score.

Check missing data and unusual values

In Analyze > Descriptive Statistics > Frequencies, review values outside the valid range and the number of missing observations. An incorrectly entered value such as 55 instead of 5 can change the mean substantially, while the median may be less affected. Correct it to the original value if you have evidence from the questionnaire, or record and handle it according to the rule stated in the methodology.

Examine the distribution and percentiles

Run Explore to view the boxplot, percentiles, and extreme observations. If the median is low because most respondents genuinely selected low levels, that is a result to report, not a software error. Remove an observation only when you have a predetermined criterion, such as a questionnaire with substantial missing data or a value outside the possible range.

Do not choose the cutoff arbitrarily

If you use the median to divide low and high groups, state clearly how observations equal to the median were handled. For example, you may create two groups using the conditions less than or equal to the median and greater than the median, but the two groups may not contain equal numbers of observations. Changing the cutoff repeatedly to obtain a more attractive p-value will be difficult to explain to your supervisor.

EFA, regression, t-test, and other analyses should not be decided by the median alone. If a variable has a low median but still measures the intended concept and fits the model, you should not remove it merely because it differs from your initial expectation. When you need to assess the scale, also review the variance calculation formula and the complete set of related output tables instead of changing one number in isolation.

Distinguishing the Median from the Mean and Quartiles

The median and the mean both describe central tendency, but they react differently to data. The arithmetic mean uses every value and can be pulled strongly by an outlier. The median is based on the position of the data after sorting, so it is usually more resistant to a few extreme values.

For example, the set 2, 3, 4, 5, 30 has a median of 4 but a mean of 8.8. If 30 is an input error, check the data source. If 30 is a genuine observation, the median may describe the typical group more effectively, while the mean still shows the overall level when every value is included.

Quartiles are points that divide the data into four parts. Q1 is the 25th percentile, the median corresponds to Q2 or the 50th percentile, and Q3 is the 75th percentile. The interquartile range, written as IQR, equals Q3 - Q1. IQR shows the width of the central 50% of the data and is often used with a boxplot to examine outliers.

You can present all three indicators as follows: “The median of [VARIABLE NAME] is [M], with Q1 equal to [Q1] and Q3 equal to [Q3]. The interquartile range is [IQR], indicating that the central 50% of observations lie between [Q1] and [Q3].” Do not call Q1 or Q3 the mean of a group of data, because they are positional points.

Common Errors When Using the Median

Confusing the median with the most frequent value

The most frequent value is the mode. A dataset can have a median of 4 but a mode of 5. The two indicators answer different questions, so check the column name in the output carefully.

Sorting incorrectly before calculating manually

If you calculate the median by hand, sort the data first. Choosing a value that appears to be in the middle of the original data table produces an incorrect result because the data-entry order does not represent statistical position.

Using the median as a general quality threshold

A median of 3.2 is not automatically low, and a median of 4.5 is not automatically good. The interpretation depends on the scale, the concept, and the research objective.

Reporting only the median and ignoring the number of observations

A median calculated from 180 observations and a median calculated from 8 observations do not have the same level of persuasive strength. Report the valid N, the number of missing observations, and appropriate dispersion indicators.

Changing data to make the median look better

You can check and correct data-entry errors, but you must not change valid responses simply to obtain a desired value. If you remove an observation, state the criterion, number, and reason clearly in the methodology or results section.

Frequently asked questions

What is the median and what is the median value?

The median is the indicator located in the middle of a number sequence after the data have been sorted. The median value is the specific value of that indicator. With an odd number of observations, take the middle value. With an even number of observations, take the mean of the two middle values.

What median value is good?

There is no single good median for every variable. With a 1 to 5 Likert scale, you can compare the median with the midpoint of 3 and interpret it according to the research objective. Read the median together with the scale labels, frequencies, and other descriptive indicators.

Is the median the same as the mean?

The median and the mean both describe the central position, but they are not the same. The arithmetic mean uses every value and is sensitive to outliers, while the median is based on order and is usually less affected by a few extreme values.

When should you use the median instead of the mean?

Consider the median when the data are strongly skewed, contain outliers, or are measured on an ordinal scale. If the data distribution is relatively symmetric, the mean and standard deviation can still be useful. The final decision must fit the research design and the selected analysis method.

What should you do if SPSS does not show the median?

Go to Analyze > Descriptive Statistics > Frequencies, move the variable to the Variable(s) box, select Statistics, check Median, then select Continue and OK. If it still does not appear, check that the variable was entered in numeric form and that you are viewing the Statistics table rather than a separate frequency table.

Open your SPSS file again, run Frequencies or Explore, record the valid N, median, Q1, Q3, and unusual values, then use the Statistics topic to compare your interpretation before writing the results chapter. If you need to run the complete analysis on your own .sav or .csv file, see DoThesis M4 data analysis.