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- Title
A note on the "Sum of squares of deviations".
- Authors
Simon, John T.
- Abstract
Dear Editor: In proposing that students be encouraged to explore possible sample measures of variability, Bukac and Sulc [1] suggest one that does not require the assumption of a measure of center, in particular the mean, namely the sum of squares of all differences between observations. For example, the textbook by Hays [2] states that "the variance is directly proportional to the average squared difference between all pairs of observation" (p. 186) - this captures the essence of the idea, but the formula given there is different: HT <math display="block" overflow="scroll" altimg="urn:x-wiley:0141982X:media:test12238:test12238-math-0001" xmlns="http://www.w3.org/1998/Math/MathML"><munder><mo movablelimits="false"> </mo><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></munder><mfrac><msup><mfenced open="(" close=")"><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>-</mo><msub><mi>x</mi><mi>j</mi></msub></mrow></mfenced><mn>2</mn></msup><mfenced open="(" close=")">N2</mfenced></mfrac><mo>=</mo><mfrac><mrow><mn>2</mn><mi>N</mi></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></mfrac><msup><mi>S</mi><mn>2</mn></msup><mo>.</mo></math> ht From the context of discussion in Hays [2], we see that the summation is over distinct pairs, that is, for I i i from 1 to I N i - 1, and I j i from I i i + 1 to I N i .
- Subjects
SUM of squares
- Publication
Teaching Statistics, 2021, Vol 43, Issue 1, p44
- ISSN
0141-982X
- Publication type
Article
- DOI
10.1111/test.12238