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Table 1 Distribution of digits in a sample of 8000 values with mean 39.61500

From: How many of the digits in a mean of 12.3456789012 are worth reporting?

Decade

Digit

mIQ

0

1

2

3

4

5

6

7

8

9

A: SEM 1.33a

 10’s

4954

3046

889

 1’s

1900

836

267

36

10

23

180

713

1727

2309

496

 0.1’s

785

785

764

841

807

751

827

851

813

776

193

 0.01’s

816

773

798

787

810

830

784

794

816

792

100

 0.001’s

849

782

809

818

766

790

820

792

775

799

133

 0.0001’s

809

789

781

817

815

782

831

803

771

802

107

B: SEM 0.0133 (only 1/100 that in A above)

 10’s

8000

1000

 1’s

8000

1000

 0.1’s

950

7050

889

 0.01’s

1845

2330

1838

808

200

29

3

23

177

747

503

 0.001’s

823

802

828

783

790

770

831

786

787

800

117

 0.0001’s

818

766

822

812

778

796

814

823

793

778

124

 0.00001’s

788

834

788

817

788

839

841

807

741

757

101

  1. Values drawn randomly from a Gaussian (‘normal’) population with mean 39.61500 and SEM as shown. The target digit in each decade is in italic; the most frequent digit in each row/decade is underlined. ‘–’ represents ‘0’. The sample of 8000 is an arbitrary choice that gives cell entries (in the lower rows) three digits. One measure of inequality along a row is IQ (the standardised sum of absolute differences from the row mean, range 0–1, see text), presented here multiplied by 1000 as mIQ
  2. aBy the 0.1’s the target digit is not the most frequent