Summary statistics of a data set – dragging data points
MathematicsStatisticsAges 15–16
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Statistics
A data sample is shown as a dot plot on a number line. Drag any point (or click 'Random') and watch the mean, median, quartiles Q₁, Q₂, Q₃, mode, range, interquartile range, variance and standard deviation update instantly. A box plot is drawn below, with outliers (outside [Q₁ − 1.5·IQR; Q₃ + 1.5·IQR]) marked with ×; drag one point far away to see the mean shift a lot while the median barely changes. Extra views: sample SD (n − 1) versus population SD (n), coding y = a·x + b, outlier rules with data cleaning, and stem-and-leaf plots (single and back-to-back).
Lesson: Measures of central tendency and measures of spread
What it shows
A small data set is plotted as dots on a number line, with measures of centre (mean, median, mode) and spread (range, IQR, variance, standard deviation) recalculated as the data change. The sample SD s divides by n − 1 and the population SD σ by n; a menu shows either or both. Other views show coding (y = a·x + b shifts the centre by b and scales the spread by |a|), outlier rules (1.5·IQR fences or mean ± 2 or 3 SD) with data cleaning, and single or back-to-back stem-and-leaf plots. One extreme value moves the mean and SD strongly; the median and IQR resist it.
How to use
Drag a dot far to the right and record how the mean, median, SD and IQR change; Random makes a new sample of size n. Choose Coding: y = a·x + b and move the a and b sliders to compare x and y. In Outliers and data cleaning, pick a rule, press Messy data example, then Remove outliers. Stem-and-leaf plot shows the data by tens; tick Back-to-back with data set B. Reset returns to the starting data.
Parameters you can change
- Sample size n (when generating randomly) 5–20
- Sample data (comma-separated; leave blank = random)
- Maximum value on the axis 10–100
- Show box plot
- View Summary statistics, Coding y = a·x + b, Outliers and data cleaning, Stem-and-leaf plot
- Standard deviation divisor Show both (n − 1 and n), Sample: n − 1, Population: n
- Coding: multiply by a -3–3
- Coding: add b -20–20
- Outlier rule 1.5 × IQR fences, Mean ± 2 SD, Mean ± 3 SD
- Data set B for the back-to-back stem-and-leaf plot (blank = random)
- Back-to-back stem-and-leaf plot
Questions to explore
- In the default data set, why is the value 25 marked as an outlier?
- Which summary measures change least when you drag one point far away from the rest?
- Can two data sets with the same range have different standard deviations, and can you build an example?
