Count
0
Number of observations
Live Summary
Mean
0
Arithmetic average
Median
0
Middle ordered value
Mode
None
Most frequent value(s)
Range
0
Max - min
Variance
0
Average squared spread
Std. Dev.
0
Typical distance from mean
IQR
0
Q3 - Q1
Layered Visualization Window
Distribution points, histogram bars, and box plot summaries now share one large window. Use the toggles to display one view or overlap them.
Mean
Median
Data points
Histogram
Outlier
Turn Spray Data on, then click or drag inside the window to add jittered observations.
What Changed?
Load data to see how the center and spread behave.
| Statistic | Value | Interpretation |
|---|
Five-Number Summary
Shape notes will appear here after calculation.
Center Formulas
Spread Formulas
Concept Builder
Mean
The mean uses every value, so it is powerful but sensitive to unusually high or low numbers.
- Best when data are roughly symmetric.
- Moves quickly when outliers appear.
- Pairs naturally with standard deviation.
Median
The median is the middle of the ordered data, so it resists distortion from extreme values.
- Best for skewed data and outliers.
- Pairs naturally with IQR.
- Represents a typical middle observation.
Mode
The mode identifies the most frequent value or values, which is useful for repeated categories or clusters.
- Can be one value, many values, or none.
- Useful when repeated outcomes matter.
- Not always informative for continuous data.
Range and IQR
Range uses only the extremes, while IQR focuses on the middle 50% of the data.
- Range is easy but very outlier-sensitive.
- IQR is robust and box-plot friendly.
- Use IQR to discuss spread without the tails dominating.
Variance and Standard Deviation
Variance squares distances from the mean, and standard deviation brings that spread back into the original units.
- Large values mean data are widely spread.
- Works best with the mean.
- Sample and population formulas are slightly different.
MAD
Mean absolute deviation measures average distance from the mean without squaring the distances.
- More intuitive than variance.
- Less harsh on outliers than variance.
- Great for classroom interpretation.
Quick Decision Guide
| Situation | Recommended Pair |
|---|---|
| Roughly symmetric data with no major outliers | Mean + standard deviation |
| Skewed distribution or extreme outliers | Median + IQR |
| Repeated popular value matters most | Mode + frequency view |
| You want an easy first spread measure | Range, then compare with IQR |
Interpretive Rules of Thumb
If mean is much larger than median, the data are often right-skewed. If mean is much smaller than median, the data are often left-skewed.
If range is huge but IQR stays modest, the middle of the data may be stable while the tails contain outliers.
Two datasets can share the same mean and have very different standard deviations, so center alone is never the whole story.