Table-Based Distribution Sets

At a glance 10 rules

1. 1Share to count$\text{count} = \dfrac{\text{share}\ \%}{100} \times \text{total}$$\text{missing share} = 100\% - \text{the rest}$
2. 2Share of a share$x\% \text{ of } y\% \text{ of } N = \dfrac{x \times y \times N}{10000}$
3. 3Moving between headsWhen one head grows out of another (more rent paid from savings), the total stays put: add the change to one share and take it from the other.
4. 4Share vs countWhen the total changes, compare counts, not shares: a count falls only if its new share is below old share × old total ÷ new total.
5. 5Overall share$\text{overall}\ \% = \dfrac{p_1 n_1 + p_2 n_2}{n_1 + n_2}$$p = \text{share in the group},\ n = \text{its size}$
6. 6Two-way tableEvery row and column adds up to its total; fill a line with one blank first. Then read the base: 'of the non-vegetarians' and 'of the second years' differ.
7. 7Running-count tablesIn a 'below x' or an 'x and above' table, a band's count is the difference between the two rows at its edges.
8. 8Unchanged group anchorsIf one group's count does not change, its new share fixes the new total: new total = that count ÷ its new share.
9. 9Band edgesValues inside a band can sit anywhere in it. For the least possible count above a cut, push the band's members below the cut; for the most, push them above.
10. 10Least overlap$\text{both} \ge A + B - N$$A, B = \text{groups},\ N = \text{all};\ \text{most} = \min(A, B)$