Prognostic value of university entrance examinations in Scotland.

Date:
1934
Catalogue details

Licence: In copyright

Credit: Prognostic value of university entrance examinations in Scotland. Source: Wellcome Collection.

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    APPENDIX IV Note on STATISTICAL TERMS USED IN THIS REPORT The mean of a set of values is found, as every schoolboy knows, by dividing their sum by their number. It is a measure of the central tendency of the group. For the benefit of the lay reader who is unfamiliar with statistical methods, it may be advisable to point out that the median is another measure of central tendency; it is the middle value when all the values are arranged in descending order of magnitude; it is quickly found, it is useful where (as in Table V) the values are not expressed numerically, and it usually has nearly the same value as the mean. Two sets of marks may differ in another respect, namely, in scatter (called also dispersion); in one set the individual marks may cluster closely round the mean, whereas in the other they may be widely scattered; for example, two sets of marks may have actually the same mean, 60, but in one set they may range from 55 to 65, while in the other they may run from 40 to 80. The most commonly used measure of this scatter is the standard deviation (c); it is the square root of the mean of the squares of the differences between the individual values and their mean. If 2 be the number of values, and x be the difference between their mean and one of them, then jae) In Table XX XIX the mean mark of the men who took Honours in subjects other than Mathematics was 64:28, which is nearly the same as 63-94, the mean mark of the women; but the standard deviation of the women was greater, showing that there was greater variability in their marks. The probable error (P.E.) is another measure of dispersion. It is about two-thirds (more exactly -6745) of the standard devia- tion. In a normal distribution half of the values lie between the limits (Mean + P.E.) and (Mean — P.E.), while -68 of them lie between the limits (Mean +) and (Mean — 0). For a full explanation of the meaning and use of the standard