Feet and height

A class of children measured each other and found a rule of thumb: the length of a foot is about fifteen hundredths of a person's height. A rule of thumb is a rough guide, not a law.

A class found a rule of thumb: foot length $f\approx 0.15h$, where $h$ is the height. (Rough, not a law.)

Rule: $f\approx 0.15h$.

Five children measured their height and their foot, all in centimetres: height 120, foot 18; height 130, foot 20; height 140, foot 21; height 150, foot 23; height 160, foot 24.

$(h,f)$ in cm: $(120,18),(130,20),(140,21),(150,23),(160,24)$. The ratio always satisfies $0.15\le \frac{f}{h}\le 0.154$.

$(h,f)$: $(120,18),(130,20),(140,21),(150,23),(160,24)$.

To test the rule they turned it round: height should be the foot divided by fifteen hundredths, which is about six and two thirds feet. The rule guessed 120, 133, 140, 153 and 160. Every guess was less than four centimetres out.

Turned round: $h\approx \frac{f}{0.15}$, and $\frac{1}{0.15}\approx 6.7$ feet. Guesses $120,133,140,153,160$, each out by less than $4$.

$h\approx \frac{f}{0.15}$, error $<4$.

Then the teacher found a bare footprint on the damp floor by the sink, twenty-five and a half centimetres long. The rule said one hundred and seventy. The owner was measured the next day: one hundred and seventy-two. The guess was two centimetres out.

A footprint $f=25.5$: $h\approx \frac{25.5}{0.15}=170$. Measured: $172$. Error $2\le 4$.

$f=25.5$, so $h\approx 170$; measured $172$.

Remember, though, that children are still growing, and for one particular person a rule of thumb may be wrong. Rule of thumb means roughly.

Children keep growing; for one person the rule may be wrong.

Error $e\ne 0$ is possible.