InternationalMathematical, physical and chemical tablesTables for Crystallography Volume C Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C, ch. 9.6, pp. 813-814
## Section 9.6.2.4. Statistics |

Where there are less than four independent observations of a given bond length, then each individual observation is given explicitly in Table 9.6.3.3. In all other cases, the following statistics were generated by the program *STATS*.

The statistics given in Table 9.6.3.3 correspond to distributions for which the automatic 4σ cut-off (see above) had been applied, and any manual removal of additional outliers (an infrequent operation) had been performed. In practice, a very small percentage of observations were excluded by these methods. The major effect of removing outliers is to improve the sample standard deviation, as shown in Fig. 9.6.2.1(*b*)
in which four (out of 366) observations are deleted.

The statistics chosen for tabulation effectively describe the distribution of bond lengths in each case. For a symmetrical, normal distribution, the mean (*d*) will be approximately equal to the median (*m*), the lower and upper quartiles () will be approximately symmetric about the median , and 95% of the observations may be expected to lie within ±2σ of the mean value. For a skewed distribution, *d* and *m* may differ appreciably and and will be asymmetric with respect to *m*. When a bond-length distribution is negatively skewed, *i.e.* very short values are more common than very long values, then it may be due to thermal-motion effects; the distances used to prepare the table were not corrected for thermal libration.

In a number of cases, the initial bond-length distribution was clearly not unimodal as in Fig. 9.6.2.1(*a*). Where possible, such distributions were resolved into their unimodal components (as in Fig. 9.6.2.1*c*) on chemical or structural criteria. The case illustrated in Fig. 9.6.2.1, for Cu—Cl bonds, is one of the most spectacular examples, owing to the dramatic consequences of oxidation state and coordination number (and Jahn–Teller effects) on the structures of copper complexes.

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