| \[Mean\] | \[\bar{x}=\frac{\sum x}{n}\] |
\[x\,=\, Observations \,given\] \[n\, =\, Total\, number\, of\] \[observations\] |
|---|---|---|
| \[Median\] |
\[If\, n\, is\, odd,\, then\] \[M\,=(\frac{n+1}{2})\,term\] \[If\, n\, is\, even,\, then\] \[M \,=\,\frac{(\frac{n}{2})^{th}term+(\frac{n}{2}+1)^{th}term}{2}\] |
\[n \,= \,Total\, number \,of\] \[observations\] |
| \[Mode\] |
\[The\, value\, which\, occurs\]
\[most\, frequently\] |
\[-\] |
| \[Variance\] | \[\sigma ^{2}\,=\,\frac{\sum (x-\bar{x})^{2}}{n}\] |
\[x\, =\, Observations\, given\] \[x¯\, =\, Mean\] \[n \,= \,Total\, number \,of\] \[observations\] |
| \[Standard \,Deviation\] | \[S = \sigma = \sqrt{\frac{\sum (x-\bar{x})^{2}}{n}}\] |
\[x\, =\, Observations\, given\] \[x¯\, =\, Mean\] \[n \,= \,Total\, number \,of\] \[observations\] |
| \[Range\] | \[L-S\] |
\[L\, =\, Largest\, value\] \[S\, =\, Smallest\, value\] |
| \[Coeff.\,of\,Range\] | \[\frac{L-S}{L+S}\] |
\[L\, =\, Largest\, value\] \[S\, =\, Smallest\, value\] |
| \[Coeff.\,of\,Variation\] | \[\frac{\sigma}{\bar{x}}*100\] |
\[\sigma=Standard\, Deviation\] \[x¯\, =\, Mean\] |
| \[Combined \,Mean\] | \[\frac{m\bar{x}\,+\,n\bar{y}}{m+n}\] |
\[x¯\,/y¯\, =\, Mean\, of\, two\] \[distributions\] \[m\,/n\,=no.\,of\,elements\,in\,\] \[each\,distributions\] |
| \[Weighted\,Mean\] | \[\frac{\sum Wi\,xi}{\sum Wi}\] |
\[Wi=Weight \,of\, each\] \[distributions\] \[xi=ith\,observation\] |
|
\[Mean\,Deviation\] \[about\,mean\] \[\bar{X}\] |
\[\frac{\sum|xi-\bar{x}|}{n}\] |
\[n \,= \,Total\, number \,of\] \[observations\] \[x¯\, =\, Mean\] \[xi=ith\,observation\] |
|
\[Mean\,Deviation\] \[about\,median\] \[M\] |
\[\frac{\sum|xi-M|}{n}\] |
\[n \,= \,Total\, number \,of\] \[observations\] \[M\, =\, Median\] \[xi=ith\,observation\] |
|
\[Mean\,Deviation\] \[about\,mode\] \[Z\] |
\[\frac{\sum|xi-Z|}{n}\] |
\[n \,= \,Total\, number \,of\] \[observations\] \[Z\, =\, Mode\] \[xi=ith\,observation\] |
|
\[Mean\,Deviation\] \[about\,any\,no.\,'a'\] |
\[\frac{\sum|xi-a|}{n}\] |
\[n \,= \,Total\, number \,of\] \[observations\] \[xi=ith\,observation\] |
|
\[For \,symmetrical \] \[Distribution:\] |
\[Mode\,=\,3Median\,-\,2Mean\] | \[-\] |