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DESCRIPTIVE STATISTICS
Descriptive Statistics
Enter a dataset to compute the full five-number summary, dispersion, shape, z-scores, and outliers — with a box plot and normal curve. Try a cosmic example below.
COUNT (n)12
SUM (Σx)20
MEAN (x̄)1.6667
MEDIAN1.5
MODENo mode
MIN0.8
MAX3.4
RANGE2.6
Q1 (25th pct)1.075
Q3 (75th pct)2.025
IQR0.95
VARIANCE (population)0.5822
VARIANCE (sample)0.6352
STD DEV (population)0.763
STD DEV (sample)0.797
COEF. OF VARIATION %47.82
SKEWNESS1.095
EXCESS KURTOSIS0.649
FIVE-NUMBER SUMMARY & BOX PLOT
min 0.8Q1 1.08med 1.5Q3 2.03max 3.4
Green line = median · dashed purple = mean · red dots = outliers
NORMAL CURVE (SAMPLE STD DEV)
Z-SCORES
0.8 → z=-1.090.9 → z=-0.961 → z=-0.841.1 → z=-0.711.2 → z=-0.591.4 → z=-0.331.6 → z=-0.081.7 → z=0.042 → z=0.422.1 → z=0.542.8 → z=1.423.4 → z=2.17
WORKED SOLUTION
Mean: x̄ = Σx / n = 20 / 12 = 1.6667
Sample variance: s² = Σ(x − x̄)² / (n − 1) = 6.9867 / 11 = 0.6352
Sample std dev: s = √s² = √0.6352 = 0.797
IQR: Q3 − Q1 = 2.025 − 1.075 = 0.95
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