Descriptive summary (mean, SD, SE, quartiles)
Shown in the app as descriptive_summary. Part of the method reference, under Descriptive.
When to use
Summarise one or more chosen NUMERIC columns as numbers: n, missing, mean, standard deviation, variance, standard error of the mean with a t-based confidence interval, median, quartiles (R quantile type 7), IQR and range - optionally split by one grouping variable. Each variable uses its own non-missing values. No hypothesis is tested.
What you provide
- The numeric variables to summarise: one or more numeric columns.
- Group (optional): one categorical column.
Options
Missing data
- Complete case (listwise deletion)
Multiple comparisons
- Not adjustable for this method. Where it makes post-hoc comparisons, the procedure applies its own correction.
Confidence level
Every interval in the result is reported at the level you choose:
- 90%
- 95%
- 99%
Related methods
Other methods under Descriptive:
How to read the output
The descriptive summary describes one or more numeric columns you choose, as numbers rather than formatted text: for each column it reports the number of values (n), the number missing, the mean, the standard deviation (SD), the variance, the standard error of the mean (SE), a confidence interval for the mean with its margin of error and the t critical value behind it, the median, the first and third quartiles (Q1, Q3), the interquartile range (IQR), and the minimum and maximum. You can split the summary by one grouping column; each column then gets an Overall row followed by one row per group. No hypothesis is tested, so there is no p-value.
SD and SE answer different questions. The SD describes how spread out individual values are. The SE describes how precisely the mean is estimated, and it shrinks as the sample grows (it is the SD divided by the square root of n). The confidence interval of the mean is built from the SE: the mean plus or minus the t critical value for n - 1 degrees of freedom times the SE. The level is 95% by default and can be set to 90% or 99%. Results show SD and SE in separate, named columns rather than as “mean +/- something”, because a bare plus-or-minus is often read the wrong way.
Quartiles use R’s quantile type 7, which is R’s default and is named in the output and in the Methods sentence. There are several standard ways to compute a sample quartile, and other software can give slightly different quartiles on the same data, especially in small samples.
Missing values are handled per column. Each column is summarised on its own non-missing values, so one column’s numbers never depend on which other columns you selected, and two columns with different missing values can report a different n. A row whose group value is missing still counts in the Overall row. With a single value there is no spread, so the SD, SE and interval are shown as “-”; a column whose values are all equal has an SD of 0.
When to use the descriptive table instead. For categorical columns, or for a formatted Table 1 that chooses a mean (SD) or a median [Q1, Q3] per variable and reports counts with confidence intervals for proportions, use the descriptive table (Table 1). A 0/1 column can be summarised here (its mean is a proportion), but the descriptive table is where a proportion gets its proper interval.
Sources: Hyndman RJ, Fan Y (1996), Sample quantiles in statistical packages, The American Statistician 50(4):361-365, doi:10.1080/00031305.1996.10473566.
Worked examples
Celeus's result on a published or illustrative dataset, next to an independent computation and, where one exists, a published value. The data themselves are not reproduced here.
the integers 1 to 10
- Source: Illustrative or synthetic example data
- Licence: synthetic (no third-party content)
- Reference: Hand computation on the integers 1 to 10; not published data
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Number of non-missing values, summary row 1 | 10 | 10 | - | Yes |
| Mean, summary row 1 | 5.5 | 5.5 | - | Yes |
| Median, summary row 1 | 5.5 | 5.5 | - | Yes |
| First quartile (Q1), summary row 1 | 3.25 | 3.25 | - | Yes |
| Third quartile (Q3), summary row 1 | 7.75 | 7.75 | - | Yes |
| Minimum, summary row 1 | 1 | 1 | - | Yes |
| Maximum, summary row 1 | 10 | 10 | - | Yes |
| Standard deviation (SD), summary row 1 | 3.02765 | 3.02765 | - | Yes |
| Standard error of the mean (SE), summary row 1 | 0.957427 | 0.957427 | - | Yes |
| Lower confidence limit of the mean, summary row 1 | 3.33415 | 3.33415 | - | Yes |
| Upper confidence limit of the mean, summary row 1 | 7.66585 | 7.66585 | - | Yes |
datasets::morley
- Source: Published dataset distributed with an R package
- Licence: base R (GPL)
- Reference: Michelson (1882), Astronomical Papers 1:109-145
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Number of non-missing values, summary row 1 | 100 | 100 | - | Yes |
| Mean, summary row 1 | 852.4 | 852.4 | - | Yes |
| Median, summary row 1 | 850 | 850 | - | Yes |
| First quartile (Q1), summary row 1 | 807.5 | 807.5 | - | Yes |
| Third quartile (Q3), summary row 1 | 892.5 | 892.5 | - | Yes |
| Minimum, summary row 1 | 620 | 620 | - | Yes |
| Maximum, summary row 1 | 1070 | 1070 | - | Yes |
| Standard deviation (SD), summary row 1 | 79.0105 | 79.0105 | - | Yes |
| Standard error of the mean (SE), summary row 1 | 7.90105 | 7.90105 | - | Yes |
| Lower confidence limit of the mean, summary row 1 | 836.723 | 836.723 | - | Yes |
| Upper confidence limit of the mean, summary row 1 | 868.077 | 868.077 | - | Yes |
datasets::morley Speed on the NIST Michelso scale (km/s)
- Source: Published dataset distributed with an R package
- Licence: base R (GPL)
- Reference: Michelson (1882), Astronomical Papers 1:109-145. NIST Statistical Reference Datasets (Standard Reference Database 140), DOI 10.18434/T43G6C
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Number of non-missing values, summary row 1 | 100 | 100 | - | Yes |
| Mean, summary row 1 | 299.852 | 299.852 | 299.852 | Yes |
| Median, summary row 1 | 299.85 | 299.85 | - | Yes |
| First quartile (Q1), summary row 1 | 299.808 | 299.808 | - | Yes |
| Third quartile (Q3), summary row 1 | 299.892 | 299.892 | - | Yes |
| Minimum, summary row 1 | 299.62 | 299.62 | - | Yes |
| Maximum, summary row 1 | 300.07 | 300.07 | - | Yes |
| Standard deviation (SD), summary row 1 | 0.0790105 | 0.0790105 | 0.0790105 | Yes |
| Standard error of the mean (SE), summary row 1 | 0.00790105 | 0.00790105 | - | Yes |
| Lower confidence limit of the mean, summary row 1 | 299.837 | 299.837 | - | Yes |
| Upper confidence limit of the mean, summary row 1 | 299.868 | 299.868 | - | Yes |
datasets::morley
- Source: Published dataset distributed with an R package
- Licence: base R (GPL)
- Reference: Michelson (1882), Astronomical Papers 1:109-145
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Number of non-missing values, summary row 1 | 100 | 100 | - | Yes |
| Mean, summary row 1 | 852.4 | 852.4 | - | Yes |
| Median, summary row 1 | 850 | 850 | - | Yes |
| First quartile (Q1), summary row 1 | 807.5 | 807.5 | - | Yes |
| Third quartile (Q3), summary row 1 | 892.5 | 892.5 | - | Yes |
| Minimum, summary row 1 | 620 | 620 | - | Yes |
| Maximum, summary row 1 | 1070 | 1070 | - | Yes |
| Standard deviation (SD), summary row 1 | 79.0105 | 79.0105 | - | Yes |
| Standard error of the mean (SE), summary row 1 | 7.90105 | 7.90105 | - | Yes |
| Lower confidence limit of the mean, summary row 1 | 839.281 | 839.281 | - | Yes |
| Upper confidence limit of the mean, summary row 1 | 865.519 | 865.519 | - | Yes |
datasets::morley
- Source: Published dataset distributed with an R package
- Licence: base R (GPL)
- Reference: Michelson (1882), Astronomical Papers 1:109-145
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Number of non-missing values, summary row 1 | 100 | 100 | - | Yes |
| Mean, summary row 1 | 852.4 | 852.4 | - | Yes |
| Median, summary row 1 | 850 | 850 | - | Yes |
| First quartile (Q1), summary row 1 | 807.5 | 807.5 | - | Yes |
| Third quartile (Q3), summary row 1 | 892.5 | 892.5 | - | Yes |
| Minimum, summary row 1 | 620 | 620 | - | Yes |
| Maximum, summary row 1 | 1070 | 1070 | - | Yes |
| Standard deviation (SD), summary row 1 | 79.0105 | 79.0105 | - | Yes |
| Standard error of the mean (SE), summary row 1 | 7.90105 | 7.90105 | - | Yes |
| Lower confidence limit of the mean, summary row 1 | 831.649 | 831.649 | - | Yes |
| Upper confidence limit of the mean, summary row 1 | 873.151 | 873.151 | - | Yes |
datasets::ToothGrowth
- Source: Published dataset distributed with an R package
- Licence: base R (GPL)
- Reference: Crampton (1947), J. Nutrition 33(5)
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Number of non-missing values, summary row 1 | 60 | 60 | - | Yes |
| Mean, summary row 1 | 18.8133 | 18.8133 | - | Yes |
| Median, summary row 1 | 19.25 | 19.25 | - | Yes |
| First quartile (Q1), summary row 1 | 13.075 | 13.075 | - | Yes |
| Third quartile (Q3), summary row 1 | 25.275 | 25.275 | - | Yes |
| Minimum, summary row 1 | 4.2 | 4.2 | - | Yes |
| Maximum, summary row 1 | 33.9 | 33.9 | - | Yes |
| Standard deviation (SD), summary row 1 | 7.64932 | 7.64932 | - | Yes |
| Standard error of the mean (SE), summary row 1 | 0.987522 | 0.987522 | - | Yes |
| Lower confidence limit of the mean, summary row 1 | 16.8373 | 16.8373 | - | Yes |
| Upper confidence limit of the mean, summary row 1 | 20.7894 | 20.7894 | - | Yes |
| Number of non-missing values, summary row 2 | 30 | 30 | - | Yes |
| Mean, summary row 2 | 20.6633 | 20.6633 | - | Yes |
| Median, summary row 2 | 22.7 | 22.7 | - | Yes |
| First quartile (Q1), summary row 2 | 15.525 | 15.525 | - | Yes |
| Third quartile (Q3), summary row 2 | 25.725 | 25.725 | - | Yes |
| Minimum, summary row 2 | 8.2 | 8.2 | - | Yes |
| Maximum, summary row 2 | 30.9 | 30.9 | - | Yes |
| Standard deviation (SD), summary row 2 | 6.60556 | 6.60556 | - | Yes |
| Standard error of the mean (SE), summary row 2 | 1.206 | 1.206 | - | Yes |
| Lower confidence limit of the mean, summary row 2 | 18.1968 | 18.1968 | - | Yes |
| Upper confidence limit of the mean, summary row 2 | 23.1299 | 23.1299 | - | Yes |
| Number of non-missing values, summary row 3 | 30 | 30 | - | Yes |
| Mean, summary row 3 | 16.9633 | 16.9633 | - | Yes |
| Median, summary row 3 | 16.5 | 16.5 | - | Yes |
| First quartile (Q1), summary row 3 | 11.2 | 11.2 | - | Yes |
| Third quartile (Q3), summary row 3 | 23.1 | 23.1 | - | Yes |
| Minimum, summary row 3 | 4.2 | 4.2 | - | Yes |
| Maximum, summary row 3 | 33.9 | 33.9 | - | Yes |
| Standard deviation (SD), summary row 3 | 8.26603 | 8.26603 | - | Yes |
| Standard error of the mean (SE), summary row 3 | 1.50916 | 1.50916 | - | Yes |
| Lower confidence limit of the mean, summary row 3 | 13.8767 | 13.8767 | - | Yes |
| Upper confidence limit of the mean, summary row 3 | 20.0499 | 20.0499 | - | Yes |
datasets::airquality
- Source: Published dataset distributed with an R package
- Licence: base R (GPL)
- Reference: Chambers, Cleveland, Kleiner and Tukey (1983), Graphical Methods for Data Analysis
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Number of non-missing values, summary row 1 | 116 | 116 | - | Yes |
| Mean, summary row 1 | 42.1293 | 42.1293 | - | Yes |
| Median, summary row 1 | 31.5 | 31.5 | - | Yes |
| First quartile (Q1), summary row 1 | 18 | 18 | - | Yes |
| Third quartile (Q3), summary row 1 | 63.25 | 63.25 | - | Yes |
| Minimum, summary row 1 | 1 | 1 | - | Yes |
| Maximum, summary row 1 | 168 | 168 | - | Yes |
| Standard deviation (SD), summary row 1 | 32.9879 | 32.9879 | - | Yes |
| Standard error of the mean (SE), summary row 1 | 3.06285 | 3.06285 | - | Yes |
| Lower confidence limit of the mean, summary row 1 | 36.0624 | 36.0624 | - | Yes |
| Upper confidence limit of the mean, summary row 1 | 48.1962 | 48.1962 | - | Yes |
| Number of non-missing values, summary row 2 | 26 | 26 | - | Yes |
| Mean, summary row 2 | 23.6154 | 23.6154 | - | Yes |
| Median, summary row 2 | 18 | 18 | - | Yes |
| First quartile (Q1), summary row 2 | 11 | 11 | - | Yes |
| Third quartile (Q3), summary row 2 | 31.5 | 31.5 | - | Yes |
| Minimum, summary row 2 | 1 | 1 | - | Yes |
| Maximum, summary row 2 | 115 | 115 | - | Yes |
| Standard deviation (SD), summary row 2 | 22.2244 | 22.2244 | - | Yes |
| Standard error of the mean (SE), summary row 2 | 4.35857 | 4.35857 | - | Yes |
| Lower confidence limit of the mean, summary row 2 | 14.6387 | 14.6387 | - | Yes |
| Upper confidence limit of the mean, summary row 2 | 32.592 | 32.592 | - | Yes |
| Number of non-missing values, summary row 3 | 9 | 9 | - | Yes |
| Mean, summary row 3 | 29.4444 | 29.4444 | - | Yes |
| Median, summary row 3 | 23 | 23 | - | Yes |
| First quartile (Q1), summary row 3 | 20 | 20 | - | Yes |
| Third quartile (Q3), summary row 3 | 37 | 37 | - | Yes |
| Minimum, summary row 3 | 12 | 12 | - | Yes |
| Maximum, summary row 3 | 71 | 71 | - | Yes |
| Standard deviation (SD), summary row 3 | 18.2079 | 18.2079 | - | Yes |
| Standard error of the mean (SE), summary row 3 | 6.0693 | 6.0693 | - | Yes |
| Lower confidence limit of the mean, summary row 3 | 15.4486 | 15.4486 | - | Yes |
| Upper confidence limit of the mean, summary row 3 | 43.4403 | 43.4403 | - | Yes |
| Number of non-missing values, summary row 4 | 26 | 26 | - | Yes |
| Mean, summary row 4 | 59.1154 | 59.1154 | - | Yes |
| Median, summary row 4 | 60 | 60 | - | Yes |
| First quartile (Q1), summary row 4 | 36.25 | 36.25 | - | Yes |
| Third quartile (Q3), summary row 4 | 79.75 | 79.75 | - | Yes |
| Minimum, summary row 4 | 7 | 7 | - | Yes |
| Maximum, summary row 4 | 135 | 135 | - | Yes |
| Standard deviation (SD), summary row 4 | 31.6358 | 31.6358 | - | Yes |
| Standard error of the mean (SE), summary row 4 | 6.2043 | 6.2043 | - | Yes |
| Lower confidence limit of the mean, summary row 4 | 46.3374 | 46.3374 | - | Yes |
| Upper confidence limit of the mean, summary row 4 | 71.8934 | 71.8934 | - | Yes |
| Number of non-missing values, summary row 5 | 26 | 26 | - | Yes |
| Mean, summary row 5 | 59.9615 | 59.9615 | - | Yes |
| Median, summary row 5 | 52 | 52 | - | Yes |
| First quartile (Q1), summary row 5 | 28.75 | 28.75 | - | Yes |
| Third quartile (Q3), summary row 5 | 82.5 | 82.5 | - | Yes |
| Minimum, summary row 5 | 9 | 9 | - | Yes |
| Maximum, summary row 5 | 168 | 168 | - | Yes |
| Standard deviation (SD), summary row 5 | 39.6812 | 39.6812 | - | Yes |
| Standard error of the mean (SE), summary row 5 | 7.78213 | 7.78213 | - | Yes |
| Lower confidence limit of the mean, summary row 5 | 43.934 | 43.934 | - | Yes |
| Upper confidence limit of the mean, summary row 5 | 75.9891 | 75.9891 | - | Yes |
| Number of non-missing values, summary row 6 | 29 | 29 | - | Yes |
| Mean, summary row 6 | 31.4483 | 31.4483 | - | Yes |
| Median, summary row 6 | 23 | 23 | - | Yes |
| First quartile (Q1), summary row 6 | 16 | 16 | - | Yes |
| Third quartile (Q3), summary row 6 | 36 | 36 | - | Yes |
| Minimum, summary row 6 | 7 | 7 | - | Yes |
| Maximum, summary row 6 | 96 | 96 | - | Yes |
| Standard deviation (SD), summary row 6 | 24.1418 | 24.1418 | - | Yes |
| Standard error of the mean (SE), summary row 6 | 4.48302 | 4.48302 | - | Yes |
| Lower confidence limit of the mean, summary row 6 | 22.2652 | 22.2652 | - | Yes |
| Upper confidence limit of the mean, summary row 6 | 40.6313 | 40.6313 | - | Yes |
| Number of non-missing values, summary row 7 | 146 | 146 | - | Yes |
| Mean, summary row 7 | 185.932 | 185.932 | - | Yes |
| Median, summary row 7 | 205 | 205 | - | Yes |
| First quartile (Q1), summary row 7 | 115.75 | 115.75 | - | Yes |
| Third quartile (Q3), summary row 7 | 258.75 | 258.75 | - | Yes |
| Minimum, summary row 7 | 7 | 7 | - | Yes |
| Maximum, summary row 7 | 334 | 334 | - | Yes |
| Standard deviation (SD), summary row 7 | 90.0584 | 90.0584 | - | Yes |
| Standard error of the mean (SE), summary row 7 | 7.45329 | 7.45329 | - | Yes |
| Lower confidence limit of the mean, summary row 7 | 171.2 | 171.2 | - | Yes |
| Upper confidence limit of the mean, summary row 7 | 200.663 | 200.663 | - | Yes |
| Number of non-missing values, summary row 8 | 27 | 27 | - | Yes |
| Mean, summary row 8 | 181.296 | 181.296 | - | Yes |
| Median, summary row 8 | 194 | 194 | - | Yes |
| First quartile (Q1), summary row 8 | 72 | 72 | - | Yes |
| Third quartile (Q3), summary row 8 | 284.5 | 284.5 | - | Yes |
| Minimum, summary row 8 | 8 | 8 | - | Yes |
| Maximum, summary row 8 | 334 | 334 | - | Yes |
| Standard deviation (SD), summary row 8 | 115.075 | 115.075 | - | Yes |
| Standard error of the mean (SE), summary row 8 | 22.1463 | 22.1463 | - | Yes |
| Lower confidence limit of the mean, summary row 8 | 135.774 | 135.774 | - | Yes |
| Upper confidence limit of the mean, summary row 8 | 226.819 | 226.819 | - | Yes |
| Number of non-missing values, summary row 9 | 30 | 30 | - | Yes |
| Mean, summary row 9 | 190.167 | 190.167 | - | Yes |
| Median, summary row 9 | 188.5 | 188.5 | - | Yes |
| First quartile (Q1), summary row 9 | 127 | 127 | - | Yes |
| Third quartile (Q3), summary row 9 | 270.75 | 270.75 | - | Yes |
| Minimum, summary row 9 | 31 | 31 | - | Yes |
| Maximum, summary row 9 | 332 | 332 | - | Yes |
| Standard deviation (SD), summary row 9 | 92.883 | 92.883 | - | Yes |
| Standard error of the mean (SE), summary row 9 | 16.958 | 16.958 | - | Yes |
| Lower confidence limit of the mean, summary row 9 | 155.484 | 155.484 | - | Yes |
| Upper confidence limit of the mean, summary row 9 | 224.85 | 224.85 | - | Yes |
| Number of non-missing values, summary row 10 | 31 | 31 | - | Yes |
| Mean, summary row 10 | 216.484 | 216.484 | - | Yes |
| Median, summary row 10 | 253 | 253 | - | Yes |
| First quartile (Q1), summary row 10 | 175 | 175 | - | Yes |
| Third quartile (Q3), summary row 10 | 273 | 273 | - | Yes |
| Minimum, summary row 10 | 7 | 7 | - | Yes |
| Maximum, summary row 10 | 314 | 314 | - | Yes |
| Standard deviation (SD), summary row 10 | 80.5683 | 80.5683 | - | Yes |
| Standard error of the mean (SE), summary row 10 | 14.4705 | 14.4705 | - | Yes |
| Lower confidence limit of the mean, summary row 10 | 186.931 | 186.931 | - | Yes |
| Upper confidence limit of the mean, summary row 10 | 246.037 | 246.037 | - | Yes |
| Number of non-missing values, summary row 11 | 28 | 28 | - | Yes |
| Mean, summary row 11 | 171.857 | 171.857 | - | Yes |
| Median, summary row 11 | 197.5 | 197.5 | - | Yes |
| First quartile (Q1), summary row 11 | 107 | 107 | - | Yes |
| Third quartile (Q3), summary row 11 | 231 | 231 | - | Yes |
| Minimum, summary row 11 | 24 | 24 | - | Yes |
| Maximum, summary row 11 | 273 | 273 | - | Yes |
| Standard deviation (SD), summary row 11 | 76.8349 | 76.8349 | - | Yes |
| Standard error of the mean (SE), summary row 11 | 14.5204 | 14.5204 | - | Yes |
| Lower confidence limit of the mean, summary row 11 | 142.064 | 142.064 | - | Yes |
| Upper confidence limit of the mean, summary row 11 | 201.651 | 201.651 | - | Yes |
| Number of non-missing values, summary row 12 | 30 | 30 | - | Yes |
| Mean, summary row 12 | 167.433 | 167.433 | - | Yes |
| Median, summary row 12 | 192 | 192 | - | Yes |
| First quartile (Q1), summary row 12 | 116.75 | 116.75 | - | Yes |
| Third quartile (Q3), summary row 12 | 234.5 | 234.5 | - | Yes |
| Minimum, summary row 12 | 14 | 14 | - | Yes |
| Maximum, summary row 12 | 259 | 259 | - | Yes |
| Standard deviation (SD), summary row 12 | 79.1183 | 79.1183 | - | Yes |
| Standard error of the mean (SE), summary row 12 | 14.445 | 14.445 | - | Yes |
| Lower confidence limit of the mean, summary row 12 | 137.89 | 137.89 | - | Yes |
| Upper confidence limit of the mean, summary row 12 | 196.977 | 196.977 | - | Yes |
a single value
- Source: Illustrative or synthetic example data
- Licence: synthetic (no third-party content)
- Reference: Hand computation on a one-row frame; not published data
| Quantity | Celeus | Independent computation | Published value | Agrees |
|---|---|---|---|---|
| Number of non-missing values, summary row 1 | 1 | 1 | - | Yes |
| Mean, summary row 1 | 7 | 7 | - | Yes |
| Median, summary row 1 | 7 | 7 | - | Yes |
| First quartile (Q1), summary row 1 | 7 | 7 | - | Yes |
| Third quartile (Q3), summary row 1 | 7 | 7 | - | Yes |
| Minimum, summary row 1 | 7 | 7 | - | Yes |
| Maximum, summary row 1 | 7 | 7 | - | Yes |
References
- Hyndman, R. J. and Fan, Y. (1996). Sample quantiles in statistical packages. The American Statistician 50: 361-365. doi:10.1080/00031305.1996.10473566 doi:10.1080/00031305.1996.10473566