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. 2015 Feb 17;10(2):e0117972. doi: 10.1371/journal.pone.0117972

Table 1. Obtained frequencies of leading digits in textbooks and testbank.

Benford dist. Knight 3rd ed. end-of-chapter answers Young 10th ed. end-of-chapter answers Skoog 7th ed. end-of-chapter answers Knight testbank answers Knight testbank distractors combined data
# entries 1644 2155 294 1485 5671 11249
1 0.3010 0.2889 0.2858 0.3129 0.2774 0.2906 0.2883
2 0.1760 0.1673 0.1689 0.1667 0.1872 0.1816 0.1774
3 0.1249 0.1247 0.1128 0.1224 0.1428 0.1259 0.1253
4 0.0969 0.0991 0.1104 0.1122 0.0875 0.1010 0.1011
i 5 0.0791 0.0803 0.0891 0.0714 0.0714 0.0890 0.0850
6 0.0669 0.0803 0.0733 0.0646 0.0835 0.0615 0.0695
7 0.0579 0.0566 0.0617 0.0510 0.0606 0.0531 0.0562
8 0.0511 0.0535 0.0599 0.0340 0.0505 0.0474 0.0508
9 0.0457 0.0493 0.0381 0.0646 0.0391 0.0497 0.0464
MAD 1 0.0050 0.0094 0.010 0.011 0.0054 0.0033
close conform accept. conform accept. conform accept. conform close conform close conform
SSD 2 4 9 12 15 3 2
accept. conform accept. conform accept. conform accept. conform accept. conform perfect conform

1 MAD = Mean Absolute Deviation (see text for definition)

2 SSD = Sum of Square Differences (see text for definition)

Obtained distributions of leading digits and measures of conformation to Benford’s Law for three textbooks, a multiple-choice testbank, and aggregate data