Na foirmlean
Tha dà fhoirmle ann airson claonadh àbhaisteach (\(s\)).
\(s = \sqrt {\frac{{\sum {{{(X - \bar X)}^2}} }}{{n - 1}}}\) (far an e n meud an t-sampaill).
'S e an dara foirmle ath-rèiteachadh a dh'fhaodadh a dhèanamh nas fheàrr airson obrachadh a-mach.
\(s = \sqrt {\frac{{\sum {{X^2} - {{\frac{{(\sum {X)} }}{n}}^2}} }}{{n - 1}}}\) (far an e n meud an t-sampaill).
Faodaidh fear sam bith dhe na foirmlean a chleachdadh; bheir iad an aon fhreagairt dhut.
Tuilleadh mu fhoirmlean
Nuair a bhios tu a' coimeas nam foirmlean seo ri foirmlean claonadh àbhaisteach ann an leabhraichean no na d' àireamhair, 's dòcha gum faic thu \(n\) san t-seòrsaiche an àite \(n - 1\).
Nuair a bhios tu a' lorg claonadh àbhaisteach seata thomhasan, a tha dìreach nan sampall dhen t-seata iomlan de thomhasan, tha e ceart gu leòr \(n - 1\) a chleachdadh.
Nuair a tha fios aig luchd-staitistigs gu bheil iad ag obrachadh leis an t-seata iomlan no na h-àireamhan gu lèir, bidh iad a' cleachdadh \(n\) an àite \(n - 1\).
Cuimhnich gu bheil \(\sum\) a' ciallachadh 'sùim de' agus \({\bar X}\) an cuibheas.
Eisimpleir (Dòigh 1)
Lorg an cuibheas (mean) agus an claonadh àbhaisteach aig na h-àireamhan a leanas.
4, 7, 9, 11, 13, 15, 18
Freagairt
\(mean = \bar X = \frac{{(4 + 7 + 9 + 11 + 13 + 15 + 18)}}{7} = 11\)
Seo dà dhòigh air claonadh àbhaisteach (\(s\)) obrachadh a-mach, a' cleachdadh fhoirmlean.
1. A' cleachdadh \(s = \sqrt {\frac{{\sum {{{(X - \bar X)}^2}} }}{{n - 1}}}\)
| \(X\) | \({\bar X}\) | \({(X - \bar X)^2}\) |
| 4 | -7 | 49 |
| 7 | -4 | 16 |
| 9 | -2 | 4 |
| 11 | 0 | 0 |
| 13 | 2 | 4 |
| 15 | 4 | 16 |
| 18 | 7 | 49 |
| \(\sum {(X - \bar X)^2} = 138\) |
| \(X\) | 4 |
|---|---|
| \({\bar X}\) | -7 |
| \({(X - \bar X)^2}\) | 49 |
| \(X\) | 7 |
|---|---|
| \({\bar X}\) | -4 |
| \({(X - \bar X)^2}\) | 16 |
| \(X\) | 9 |
|---|---|
| \({\bar X}\) | -2 |
| \({(X - \bar X)^2}\) | 4 |
| \(X\) | 11 |
|---|---|
| \({\bar X}\) | 0 |
| \({(X - \bar X)^2}\) | 0 |
| \(X\) | 13 |
|---|---|
| \({\bar X}\) | 2 |
| \({(X - \bar X)^2}\) | 4 |
| \(X\) | 15 |
|---|---|
| \({\bar X}\) | 4 |
| \({(X - \bar X)^2}\) | 16 |
| \(X\) | 18 |
|---|---|
| \({\bar X}\) | 7 |
| \({(X - \bar X)^2}\) | 49 |
| \(X\) | |
|---|---|
| \({\bar X}\) | |
| \({(X - \bar X)^2}\) | \(\sum {(X - \bar X)^2} = 138\) |
\(s = \sqrt {\frac{138}{6}} = 4.796\,(gu\,3\,id.)\)
Ma tha duilgheadas agad leis a' chlàr, seo mar a tha e ag obrachadh:
- tha liosta dhe na h-àireamhan sa chiad cholbh
- tha an dara colbh a' lorg an diofair eadar gach àireamh agus an cuibheas
- tha an treas colbh a' ceàrnagachadh nan diofaran sin. Tha sin a' dèanamh nan àireamhan uile dearbhte
's e an ath cheum an cur-ris agus an roinn le sia (aon nas lugha na na th' ann de dh'àireamhan)
'S e an ceum mu dheireadh am freumh ceàrnagach a lorg.
Eisimpleir (Dòigh 2)
Lorg an cuibheas agus an claonadh àbhaisteach aig na h-àireamhan a leanas..
4, 7, 9, 11, 13, 15, 18
Freagairt
\(mean = \bar X = \frac{{(4 + 7 + 9 + 11 + 13 + 15 + 18)}}{7} = 11\)
A' cleachdadh an fhoirmle \(s = \sqrt {\frac{{\sum {{X^2} - {{\frac{{(\sum {X)} }}{n}}^2}} }}{{n - 1}}}\)
| \(X\) | \(X^{2}\) |
| 4 | 16 |
| 7 | 49 |
| 9 | 81 |
| 11 | 121 |
| 13 | 169 |
| 15 | 225 |
| 18 | 324 |
| \(\sum {{X^2}} = 985\) |
| \(X\) | 4 |
|---|---|
| \(X^{2}\) | 16 |
| \(X\) | 7 |
|---|---|
| \(X^{2}\) | 49 |
| \(X\) | 9 |
|---|---|
| \(X^{2}\) | 81 |
| \(X\) | 11 |
|---|---|
| \(X^{2}\) | 121 |
| \(X\) | 13 |
|---|---|
| \(X^{2}\) | 169 |
| \(X\) | 15 |
|---|---|
| \(X^{2}\) | 225 |
| \(X\) | 18 |
|---|---|
| \(X^{2}\) | 324 |
| \(X\) | |
|---|---|
| \(X^{2}\) | \(\sum {{X^2}} = 985\) |
\(s = \sqrt {\frac{{985 - \frac{{{{77}^2}}}{7}}}{6}} = \sqrt {\frac{{985 - 847}}{6}}\)
\(s = \sqrt {\frac{{138}}{6}} = 4.796\)
Mar sin 's e an claonadh àbhaisteach \(s = 4.796\), a' cleachdadh foirmle sam bith.
