Calculez la moyenne, la médiane, le mode, l’étendue, l’effectif et la somme d’une liste de nombres. Les données sont triées et les valeurs centrales sont mises en évidence.
Mis à jour Exemples vérifiés : 6
The 10 values add up to 849, so the mean is 84.9; the median is 86.5 and the mode is 92. The mean is 1.6 below the median, because the values below the median are, in total, farther from it than the values on the other side.
| Valeur | Count | Share of data | Note |
|---|---|---|---|
| 70 | 1 | 10 % | |
| 76 | 1 | 10 % | |
| 78 | 1 | 10 % | |
| 81 | 1 | 10 % | |
| 85 | 1 | 10 % | middle |
| 88 | 1 | 10 % | middle |
| 92 | 3 | 30 % | mode |
| 95 | 1 | 10 % |
The boxed value(s) sit in the middle of the sorted list.
92 appears 3 times, more often than any other value.
The mean is the sum of the values divided by how many there are. The median is the middle value once the data are sorted: the value at position (n + 1) ÷ 2 when n is odd, and the average of the two middle values when n is even. The mode is the value that occurs most often, and the range is the largest value minus the smallest.
For the 10 default quiz scores the sum is 849, so the mean is 84.9. Sorted, the 5th and 6th values are 85 and 88, which puts the median at 86.5; 92 appears three times and is the mode, and the range is 95 − 70 = 25.
Data can have several modes, all listed here, or none: when every value occurs equally often, no value is more typical than another. Standard deviation, quartiles and outliers are on the descriptive statistics calculator.
Source de vérification : Python 3.8 statistics.mean = 84.9, statistics.median = 86.5, statistics.multimode = [92]; sum 849
Source de vérification : calculator.net mean, median, mode, range calculator worked example: mean 22.143, median 23, modes 23 and 38, range 36
Source de vérification : Calculator Soup mean, median, mode calculator example output: mean 16.75, median 15.5, mode 13, range 16, count 16, sum 268
Source de vérification : NIST StRD NumAcc1 certified mean 10000002; median and range by hand from the sorted values 10000001, 10000002, 10000003
Add the values and divide by the count for the mean: 10, 2, 38, 23, 38, 23, 21 sum to 155, and 155 ÷ 7 = 22.14. Sort them (2, 10, 21, 23, 23, 38, 38) and take the middle one, the 4th, for the median: 23. Count repeats for the mode: 23 and 38 each appear twice, so both are modes. The range is 38 − 2 = 36.
Sort the values and average the two in the middle, at positions n ÷ 2 and n ÷ 2 + 1. For the 16 values 9, 10, 12, 13, 13, 13, 15, 15, 16, 16, 18, 22, 23, 24, 24, 25, the 8th and 9th are 15 and 16, so the median is 15.5. This is the definition in the NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1.
Yes to both. NIST notes that the mode is not necessarily unique: 2, 3, 3, 5, 5, 8 has two modes, 3 and 5, and is called bimodal. When every value appears the same number of times, as in 4, 7, 9 or 1, 1, 2, 2, no value occurs more often than the others and the data have no mode.
Use the mean for roughly symmetric data without extreme values, the median when a few values are far from the rest, and the mode for categories or the most common size. One outlier moves the mean but not the median: for 3, 4, 5 the mean and median are both 4, but changing 5 to 50 lifts the mean to 19 while the median stays 4.
In everyday use "average" means the arithmetic mean, the sum divided by the count, and spreadsheet functions follow that: Excel's AVERAGE returns the mean. In statistics "average" is a looser word for any measure of center, so the median and mode are also called averages. When a report says "average" without saying which, it is almost always the mean.
La précision dépend de vos données et des hypothèses de la méthode. Le calcul décimal utilise 50 chiffres significatifs, mais les estimations, méthodes numériques et données sources peuvent être moins précises ; l’arrondi affiché ne supprime pas ces limites. Exemples résolus vérifiés à partir de sources indépendantes : 6. Par exemple, « Quiz scores (default) » est vérifié à l’aide de Python 3.8 statistics.mean = 84.9, statistics.median = 86.5, statistics.multimode = [92]; sum 849.
NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1 Measures of location (mean, median, mode); NIST Statistical Reference Datasets: univariate summary statistics (NumAcc1); Python statistics module: mean, median, multimode.
Ce calculateur comprend 6 exemples résolus dont les réponses proviennent de sources indépendantes. Ils font partie de la suite de tests et peuvent aussi être exécutés ici.
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