Practical guides, how-tos and comparisons to get the most out of our free online tools.
Five incomes of 10,000 to 90,000 give a Gini of 0.38. Divide every one of them by ten and the answer is still 0.38 — the measure sees proportions and nothing else.
Camille Laurent · 3 min read
With an average of five events per interval, exactly three occur 14.0 % of the time, none at all 0.7 %, and ten or more 3.2 % — about once every 31 intervals. The distribution has one parameter, and it sets both the mean and the variance.
Daniel Okonkwo · 4 min read
The harmonic mean of 40 and 60 is 48, not 50, because the slower leg takes longer and therefore counts for more. For 1, 2 and 4 it is 1.714 against an arithmetic mean of 2.33.
Lena Hoffmann · 3 min read
For 2, 5, 7, 8, 10, 13, 18, 21, 25, 30 the range is 28, the standard deviation 9.24 and the IQR 13. Replace the last value with 300 and only the IQR survives unchanged.
Lena Hoffmann · 3 min read
At 120 BPM a quarter note lasts 500 ms, an eighth 250 and a dotted eighth 375. One division produces the whole table, and the dotted eighth is the one that changed how delay pedals are used.
Antonio Delgado · 3 min read
Three semitones above A4 is 440 × 2^(3/12) = 523.25 Hz. The twelfth root of two makes every interval slightly wrong except the octave, and that compromise is what lets a keyboard play in any key.
Antonio Delgado · 3 min read
The three digits are two figures and a count of zeros, in picofarads: 104 is 100 nF and 473 is 47 nF. The trap is 220, which is 22 pF — while a 220 pF part is marked 221.
Daniel Okonkwo · 4 min read
10 mH with 100 µF resonates at 159.2 Hz. Double the capacitance and it falls to 112.5 Hz; to halve the frequency you have to quadruple a component, because both sit under a square root.
Daniel Okonkwo · 3 min read
1,000 Ω with 100 µF gives a time constant of 0.1 s. The capacitor is 63 % charged at that point, 95 % after three constants and 99.3 % after five — the last of which is the number that matters.
Daniel Okonkwo · 3 min read
100, 220 and 330 µF in series come to 56.9 µF — less than the smallest. Put 100 µF and 1 µF in series and the total is 0.99 µF, while the small one carries 99 % of the voltage.
Daniel Okonkwo · 3 min read
25 million of revenue across 250 people is 100,000 each. Move fifty of them to a supplier and the same revenue reads 125,000 — a 25 % improvement in a productivity measure, with the same work being done.
Daniel Okonkwo · 3 min read
500,000 of liabilities against 1,200,000 of assets is 41.7 % debt, 58.3 % equity and a debt-to-equity of 0.71. The third one runs to infinity as the equity vanishes; the first cannot pass 100 %.
Camille Laurent · 3 min read