Are there cases where error and mistake are not interchangeable?
Learn English – Cases where “mistake” and “error” are not interchangeable
differencesnounssynonyms
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I think you mostly have it right, but for further exemplification, here are the most common immediately following collocates for each these words from the COCA:
Most common collocates for mandatory
1 TESTING 151
2 MINIMUM 125
3 RETIREMENT 107
4 MINIMUMS 100
5 REPORTING 87
6 SENTENCES 78
7 EVACUATION 74
8 SENTENCING 74
9 DISCLOSURE 63
10 ARBITRATION 56
11 SPENDING 41
12 DRUG 36
13 SENTENCE 35
14 EVACUATIONS 32
15 ARREST 27
16 PRISON 27
17 COUNSELING 26
18 OVERTIME 24
19 RECYCLING 23
20 BUSING 22
21 SANCTIONS 22
22 INSURANCE 21
23 SERVICE 21
24 HIV 20
25 RELEASE 20
Most common collocates for compulsory
1 EDUCATION 86
2 MILITARY 53
3 SCHOOL 31
4 SCHOOLING 21
5 STERILIZATION 19
6 LICENSING 18
7 ATTENDANCE 18
8 NATIONAL 16
9 SERVICE 15
10 MILITIA 14
11 MEMBERSHIP 14
12 JURISDICTION 11
13 HEALTH 11
14 HETEROSEXUALITY 10
15 LABOR 10
16 ARBITRATION 9
17 LICENSE 9
18 FIGURES 9
19 PROCESS 9
20 PUBLIC 9
21 RETIREMENT 8
22 DISPUTE 7
23 ARMY 7
24 VOTING 6
25 INSURANCE 6
Most common collocates for obligatory
1 SERVICE 10
2 NATURE 8
3 STOP 8
4 REFERENCE 6
5 STRUCTURE 5
6 CELIBACY 4
7 EXCHANGE 4
8 VISIT 4
9 READING 4
10 MILITARY 4
11 QUESTION 4
12 SLAP 3
13 NOD 3
14 RETURNS 3
15 BASIC 3
16 PERIOD 3
17 UPON 3
18 PHOTO 3
19 BOOK 3
20 EARLY 3
21 PARTHENOGENESIS 2
22 PREPOSITION 2
23 PILGRIMAGES 2
24 HAGGLING 2
25 ALTRUISTIC 2
As you can see, mandatory and compulsory have much stronger collocates. The collocates for mandatory are more things that are simply required by law, policy, or rule, whereas compulsory is more for specifically things that someone must do (e.g. education, military, sterilization). Obligatory, on the other hand, doesn’t have much of a strong affinity for certain things, and can be used generally for anything that is required by social custom.
The Wikipedia article explains the difference in the best way possible:
In the fields of science, engineering, industry and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's actual (true) value. The precision of a measurement system, also called reproducibility or repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. Although the two words can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method.
High accuracy, but low precision:
High precision, but low accuracy:
Best Answer
In statistics, an error is the amount that a measurement deviates from the 'true' value. Even if no mistakes are made in measuring (that is, all the right methods are used, and used correctly), there might still be error due to limited accuracy of the measurement tools, random fluctuations in the system under consideration, etc. The words are clearly not interchangeable in this context.