Data problems

A run rate is a weighted average. After 19 overs at 6 runs an over (114 runs) and a last over of 12, it is (114 + 12)/20 = 6.3.

Averages of lists of different sizes must be weighted by their sizes, as with friends who listed 6, 4, 5, 4 and 4 prices.

What changes a weighted average, and what doesn't:

• doubling every weight leaves it unchanged: the factor cancels top and bottom;
• adding the same number to every weight usually changes it, pulling it towards the plain average.

Percentages need counts before you compare. A state where 90% of schools have playgrounds need not have more such schools than a state with 78%: it may have fewer schools in all.

Shares and counts answer different questions. A play with great shares from 200 ratings is less certain than good shares from 900.

Shares must always add to 100%, so they cannot all rise, or all fall, together.