What Is the Median? How to Calculate the Median

What Is the Median and How Do You Calculate It?

You open your data file and see a series of scores, incomes, or response times with a strong skew. In that situation, the mean can be pulled upward by a few unusually large values. Calculating the median helps you identify the value in the middle of the dataset after the values have been arranged in ascending or descending order.

In English, the Vietnamese term “trung vị” is Median. If half of the observations are less than or equal to the Median and half are greater than or equal to the Median, that value is the median. You do not find the median by adding all the values and dividing by the number of observations. That is how you calculate the mean.

When the Number of Observations Is Odd

First, arrange the data from smallest to largest. With n observations, the median position is:

Median position = (n + 1) / 2

For example, a score series with 5 observations is 6, 8, 9, 12, 20. The median position is (5 + 1) / 2 = 3. The value in the third position is 9, so the Median is 9.

When the Number of Observations Is Even

If the number of observations is even, two values will lie in the middle. Take the arithmetic mean of these two values.

For example, a processing-time series contains 6 values: 4, 6, 7, 10, 12, 18. The two middle values are 7 and 10. The median is (7 + 10) / 2 = 8,5.

The general formula can be written as follows:

• If n is odd, the Median is the value at position (n + 1) / 2.
• If n is even, the Median is the arithmetic mean of the two values at positions n / 2 and n / 2 + 1.

When you are writing your thesis, you do not need to sort thousands of rows by hand. SPSS, Excel, R, and Python can all calculate the Median. The important point is understanding what this statistic describes and whether it is appropriate for the variable you are analysing.

Why the Median Matters in Quantitative Research

The median shows the central position of the data when the values are ordered. It is particularly useful when the data contain outliers, have a skewed distribution, or use an ordinal scale. For example, the incomes of 100 people may be concentrated between 8 and 15 million VND, while a few people earn 100 million VND. The mean will be pulled upward, while the median will often describe the typical group of observations more closely.

In descriptive statistics, you can report the Median together with the Minimum, Maximum, Mean, and Standard Deviation when the research question or the characteristics of the data require it. The Median is also often used to describe waiting time, the number of purchases, income, cost, or data with substantial skew.

You should examine the median together with a measure of dispersion. The Median tells you only the central position, not whether the observations are close together or widely spread. For dispersion, you can also read about standard deviation and variance. A small standard deviation usually indicates that the data are more concentrated around the mean, but the interpretation still depends on the distribution of the variable.

The median also helps you examine a pattern in a descriptive table. If the Mean is much higher than the Median, the data may be right-skewed because of several large values. If the Mean is substantially lower than the Median, the data may be left-skewed. This is a reason to inspect the chart, Minimum, Maximum, and unusual observations. It is not enough by itself to conclude that the data contain an error.

In quantitative research, do not choose the Median simply because it produces a more attractive number than the Mean. Base your choice on the type of variable, the descriptive objective, and the shape of the data. The Median has no meaningful interpretation for a nominal variable such as gender or field of study. It may be more appropriate than the Mean for an ordinal variable. For a continuous quantitative variable, you can report both the Mean and Median if you explain the reason clearly.

What Median Value Is Acceptable?

The Median has no general acceptable threshold like Cronbach's Alpha, KMO, or factor loading. It is a descriptive statistic, not a test used to decide whether a scale passes or fails. A Median of 4,2 may be appropriate in one study but meaningless unless you know the scale used for the variable and what each value represents.

The table below helps you decide how to use the Median in your report. Sources are included in rows with specific methodological criteria. For the Median itself, return to the measurement scale and the research context instead of applying a mechanical threshold.

For a 5-point Likert scale, a Median of 3 is usually interpreted as being around the neutral level, a Median of 4 as leaning toward agreement, and a Median of 5 as the highest level. You still need to check the exact labels in your questionnaire. If your scale uses 1 for strongly agree and 5 for strongly disagree, the interpretation is reversed.

The Median does not show the relationship between variables and does not prove a hypothesis. A variable with a high Median does not necessarily have a positive effect on the dependent variable. To test effects, use correlation, regression, SEM, or PLS-SEM according to your research model.

How to Read the Median in SPSS Output

If you are using SPSS, the easiest way to calculate the Median is Analyze > Descriptive Statistics > Frequencies. Move the variable you want to inspect into Variable(s), select Statistics, tick Median, then select Continue and OK. SPSS will create a Statistics table with the number of observations, minimum, maximum, mean, and median, depending on the options you selected.

You can also use Analyze > Descriptive Statistics > Explore. Move the variable into Dependent List, select Statistics if you need to adjust the descriptive information, and then click OK. The Explore command is often more useful when you also want a Boxplot, outlier information, and the distribution of the data.

Illustrative output

The table below is illustrative output, not the result of a real study. Suppose you have 120 valid questionnaire responses for the variable SAT_MEAN, which is the mean score for a satisfaction scale from 1 to 5.

The Median row, with a value of 3,7500, means that 50% of the observations have a value less than or equal to 3,75 and 50% have a value greater than or equal to 3,75, according to the position rule used by the software. Because SAT_MEAN is the mean score across several items, the Median can be a decimal even though the original items used a Likert scale from 1 to 5.

The N Valid row shows that SPSS used 120 values for the calculation. The Missing row shows that 3 values are missing. You need to check whether those missing values came from respondents leaving an item blank, incorrect coding, or a data-filtering rule. With multiple variables, the number of valid observations can differ across rows because SPSS handles missing data separately for each variable.

If you run Analyze > Descriptive Statistics > Frequencies, SPSS can also display a Frequencies table with each value, Frequency, Percent, Valid Percent, and Cumulative Percent. The Median of an ordinal variable can be identified from the cumulative frequency table. When the cumulative frequency reaches or exceeds 50%, find the corresponding value at the middle position.

You should not copy the entire output into Chapter 4. Select the statistics that serve your descriptive objective and use clear variable names. If the results table contains too many decimal places, you can round them to two decimal places, but apply the same format throughout the chapter.

How to write this in your thesis

You can adapt the following sentence to your actual output: “The descriptive statistics show that the variable [VARIABLE NAME] has a median of [MEDIAN], based on [NUMBER OF OBSERVATIONS] valid observations. This value indicates that 50% of the observations have a level [LESS THAN OR EQUAL TO] [MEDIAN] and 50% have a level [GREATER THAN OR EQUAL TO] [MEDIAN].”

If the Median is used to describe a Likert scale, you can write: “For a scale ranging from [LOWEST LEVEL] to [HIGHEST LEVEL], a Median of [MEDIAN] indicates that responses tend to be concentrated around [LEVEL LABEL], according to the coding convention of the questionnaire.” Keep this sentence only when the level labels and coding direction actually match your data.

What to Do When the Median Is Not Appropriate

First, check the type of variable. If the variable is a group code, such as 1 for male and 2 for female, a Median of 1 or 2 cannot be interpreted as the central level of gender. Use a frequency table and percentages instead.

Next, check missing values and special codes. Some files use 99, 999, or -1 to indicate “don't know” but leave SPSS treating those codes as valid values. These codes can make the Median incorrect. Declare them as missing or correct the coding rule before running the descriptive statistics again.

If the Median differs greatly from what you expected, review the original data and extreme values. Open Analyze > Descriptive Statistics > Explore, select Boxplot, or inspect the Minimum and Maximum. An outlier is not automatically an incorrect observation. Remove it only when you have a basis, such as a wrong unit, a response outside the questionnaire range, or a breach of a cleaning criterion established in advance.

If the distribution is skewed, you can report the Median instead of the Mean, or report both so that readers can see the difference. When you need to run a test, choose a method that fits the assumptions and the type of data. Switching to the Median does not fix data-entry errors, turn a nominal variable into a quantitative variable, or replace model checking.

If a Likert item has an unusually low or high Median, examine whether respondents are concentrated at one level, how the item is worded, and whether reverse coding was applied. A reverse-coded item must be coded correctly before you calculate a composite score. Keep each version of the data and record which variable was changed, why it was changed, and when it was changed.

When your supervisor asks why you used the Median, connect the answer to your data: “The author reports the Median because the variable [VARIABLE NAME] has a [RIGHT-SKEWED/LEFT-SKEWED] distribution and shows [OUTLIER DESCRIPTION]. The Median is therefore appropriate for describing the central position together with [IQR/MINIMUM AND MAXIMUM].” Use the bracketed explanation only when it matches your output.

Distinguishing the Median from the Mean, Percentile, and Mode

The Median, Mean, percentile, and Mode each describe a different aspect of a distribution and cannot replace one another.

The Mean, usually displayed as Mean, equals the sum of all values divided by the number of observations. Because the Mean uses every value, it can be strongly affected by outliers. When the data are approximately symmetric and contain no extreme values, the Mean is often the familiar measure of central tendency.

The Median, displayed as Median, is based on order and the middle position. It is less affected by a few very large or very small values. When a series contains 5 values, the Median is the third value after sorting. When it contains 6 values, the Median is the average of the third and fourth values.

A percentile, or Percentile, divides the data according to position. The 25th percentile, usually written as P25, is the point at or below which a specified proportion of observations falls according to the calculation rule used by the software. The Median corresponds to the 50th percentile, but in a report you should still call it the Median when your purpose is to describe the middle value.

The Mode is the value that appears most frequently. A variable can have one Mode, several Modes, or no clearly defined Mode. For Likert data, the Mode shows the most common response level, while the Median shows the middle position in the ordered responses.

You can also use the article about outliers if you need to check extreme observations. To review the formula and interpretation of another dispersion measure, see the variance formula. These articles supplement descriptive statistics, but they do not change the principle of choosing a statistic according to the variable type and research objective.

Common Errors When Calculating the Median

The first error is calculating the Median from an unsorted series and choosing an element in the middle. When you work manually, sort the data first. When you use SPSS, the software handles this step, but you still need to check that the variable was entered with the correct type and coding.

The second error is confusing the Median with the Mean. Many students look at the Mean column in the Descriptive Statistics table and write it down as the median. Check the row name carefully, or select Median in the Statistics dialog box before running the command.

The third error is concluding that “the Median passes” simply because it is greater than 3 on a 5-point Likert scale. The Median has no general passing threshold. A high or low value must be interpreted according to the scale labels, research question, and context.

The fourth error is ignoring missing values. If you calculate the Median in Excel and some cells are blank, the formula may produce a different result from the missing-data treatment you are using in SPSS. Set a consistent cleaning rule and confirm the number of valid observations before placing the result in your thesis.

The final error is removing an outlier only to make the Mean and Median closer. Keep the evidence, check the original record, and ask your supervisor when the decision affects sample size. Do not alter the data to produce a more convenient result.

Frequently asked questions

Is calculating the median just a matter of taking the middle number?

Yes, if the data have been sorted and the number of observations is odd. If the number of observations is even, take the arithmetic mean of the two middle numbers. This is why you should not select the middle element before sorting the data.

What Median value is acceptable?

The Median has no general acceptable level. It is a descriptive measure of central position, not a criterion for evaluating the reliability or validity of a scale. Interpret the Median according to the variable type, scale labels, and research objective.

Where do I calculate the Median in SPSS?

Go to Analyze > Descriptive Statistics > Frequencies, select the variable, click Statistics, tick Median, and run the command. If you also want a Boxplot and outlier information, use Analyze > Descriptive Statistics > Explore.

Why are the Median and Mean different?

The Mean uses the total of all observations, so it is more easily affected by very large or very small values. The Median is based on the middle position and is usually less sensitive to outliers. A large gap between the two statistics may indicate skewness, but you need to inspect the chart and extreme values as well.

Can I use the Median for a Likert scale?

Yes, particularly when you want to describe the central tendency of an ordinal variable or data with a skewed distribution. For a multi-item Likert scale, state the coding method clearly and do not use the Median as evidence that a hypothesis has been accepted.

What should I do if data are missing when I calculate the Median?

Check the amount and cause of the missing data first. You can apply the case-deletion rule or missing-data treatment specified in your research methods, but record the number of valid observations and the treatment used. Do not automatically replace every blank cell with 0 because 0 may represent a different meaningful value.

Open your SPSS file, select one variable to describe, run Analyze > Descriptive Statistics > Frequencies, and compare the Median row with N Valid, Mean, Minimum, and Maximum. Then write the result using the correct labels for your scale. If you need to run statistics on a .sav or .csv file and interpret the output, see M4 data analysis.