Interpret all statistics for Boxplot

Find definitions and interpretation guidance for every statistic that is provided with the boxplot.

N

The sample size (N) is the number of nonmissing observations for a Y variable or a group.

Minimum

The minimum is the smallest data value.

In these data, the minimum is 7.

13 17 18 19 12 10 7 9 14

Interpretation

Use the minimum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the minimum value is very low, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.

Q1

Quartiles are the three values–the first quartile at 25% (Q1), the second quartile at 50% (Q2 or median), and the third quartile at 75% (Q3)–that divide a sample of ordered data into four equal parts.

The first quartile is the 25th percentile and indicates that 25% of the data are less than or equal to this value.

For this ordered data, the first quartile (Q1) is 9.5. That is, 25% of the data are less than or equal to 9.5.

Median

The median is the midpoint of the data set. This midpoint value is the point at which half the observations are above the value and half the observations are below the value. The median is determined by ranking the observations and finding the observation that are at the number [N + 1] / 2 in the ranked order. If the number of observations are even, then the median is the average value of the observations that are ranked at numbers N / 2 and [N / 2] + 1.

For this ordered data, the median is 13. That is, half the values are less than or equal to 13, and half the values are greater than or equal to 13. If you add another observation equal to 20, the median is 13.5, which is the average between 5th observation (13) and the 6th observation (14).

Interpretation

The median and the mean both measure central tendency. But unusual values, called outliers, affect the median less than they affect the mean. When you have unusual values, you can compare the mean and the median to decide which is the better measure to use. If your data are symmetric, the mean and median are similar.

Q3

Quartiles are the three values–the first quartile at 25% (Q1), the second quartile at 50% (Q2 or median), and the third quartile at 75% (Q3)–that divide a sample of ordered data into four equal parts.

The third quartile is the 75th percentile and indicates that 75% of the data are less than or equal to this value.

For this ordered data, the third quartile (Q3) is 17.5. That is, 75% of the data are less than or equal to 17.5.

Maximum

The maximum is the largest data value.

In these data, the maximum is 19.

13 17 18 19 12 10 7 9 14

Interpretation

Use the maximum to identify a possible outlier or a data-entry error. One of the simplest ways to assess the spread of your data is to compare the minimum and maximum. If the maximum value is very high, even when you consider the center, the spread, and the shape of the data, investigate the cause of the extreme value.

Confidence interval (CI) for the median

The confidence interval provides a range of likely values for the population median. Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. But, if you repeated your sample many times, a certain percentage of the resulting confidence intervals or bounds would contain the unknown population median. The 95% confidence level indicates that, if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population median. For more information, go to What is a confidence interval?.

Interpretation

The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

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