š Math
Statistics Calculator
Analyze a dataset to determine key descriptive statistics including mean, median, mode, range, variance, standard deviation, quartiles, and interquartile range (IQR). Automatically distinguishes between sample and population statistics.
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Formula
Mean: Ī¼ = (Ī£x)/N | Sample Variance: sĀ² = Ī£(x-Ī¼)Ā²/(N-1) | Population Variance: ĻĀ² = Ī£(x-Ī¼)Ā²/NĪ£x- Sum of all values in the dataset
N- Total number of values
Ī¼- The mean of the data
Example
Basic Descriptive Statistics
Analyze the dataset: 5, 7, 9, 11, 13 (treated as a sample).
- Calculate the mean: (5+7+9+11+13)/5 = 45/5 = 9.
- Calculate the median (middle value): 9.
- Calculate the deviations from mean: -4, -2, 0, 2, 4.
- Square the deviations: 16, 4, 0, 4, 16 (Sum = 40).
- Calculate sample variance (divide by N-1=4): 40/4 = 10.
- Calculate sample standard deviation: ā10 ā 3.16.
- Result: Mean=9, Median=9, Sample SD=3.16.
Frequently Asked Questions
A population includes all members of a defined group, while a sample is a subset of that population. In statistics, sample variance divides by (N-1) to correct for bias, while population variance divides by N.