5.1 The Balancing Act — Mean as the Centre
Click anywhere below the number line to add a dot; Shift+click removes the nearest dot. The red line marks the mean. Notice that the total distance of points to the left of the mean always equals the total distance of points to the right — the mean is a true balance point!
Try building the collection 10, 10, 11, 17 (mean = 12). Then try adding a new dot far to the right — see how the mean shifts to keep the balance restored.
Will Including/Removing a Value Change the Mean?
Click below the line to add a point (Shift+click to remove the nearest one), or use the buttons. Watch how the mean moves.
Shifting & Scaling — What happens to the mean?
If a collection has mean a: adding a constant c to every value gives a new mean of a + c. Multiplying every value by k gives a new mean of k × a. Try it above and watch the "Formula check" confirm it!
Tinkering with Median
The dashed gold line marks the median — the middle value once the data is sorted. Click below the line to add a point (Shift+click removes the nearest one) and see how the median responds.
Including a value greater than the current median can push the median up; including a value less than the median can pull it down; including a value equal to the median (or values symmetrically placed) may leave it unchanged.
Mean and Median with Frequencies
Edit the frequency for each family-size value below (based on the book's example). The mean, median, and running cumulative-frequency table update live — this is how you find the median quickly without writing out every value in sorted order.
Cumulative Frequency
Finding the Unknown
Calculator 1 — The Smudged Value
Coach Balwan's data got smudged! Enter the known values (comma-separated), the total count, and the given mean — find the missing value.
w = (mean × n) − sum of known values
Calculator 2 — The Overcounted Value
Venkayya's average coconut harvest per tree was calculated with one tree's count wrongly recorded. Find the corrected average.
Spreadsheets — Totals and Averages, Live
This is a tiny working spreadsheet. Click any mark cell and edit it — the Total column
(like =SUM(...)) and the Average row (like =AVERAGE(...)) recompute
instantly.
Try changing Farooq's Maths mark and watch both his Total and the class-wide Maths average update.
5.2 Visualising Data — Line Graphs
Line graphs are great for showing change across time. Below is the book's Kerala vs Punjab monthly maximum temperature example. Toggle to a clustered-bar view to see why the line graph reads more clearly, or plot your own two data series.
Plot your own data
It's Puzzle Time! — Game of Hex
Red connects the top and bottom edges; Blue connects the left and right edges. Click a cell to place your colour — the first to build an unbroken chain between their two edges wins. (Played here on a smaller 7×7 board instead of the usual 11×11, for a quicker match.)