Editing Quartile
Latest revision | Your text | ||
Line 158: | Line 158: | ||
: <math>\text{Upper fence} = Q_3 + (1.5 \times \mathrm{IQR})</math>[[File:Boxplot outliers example.jpg|thumb|Boxplot Diagram with Outliers]] |
: <math>\text{Upper fence} = Q_3 + (1.5 \times \mathrm{IQR})</math>[[File:Boxplot outliers example.jpg|thumb|Boxplot Diagram with Outliers]] |
||
The lower fence is the "lower limit" and the upper fence is the "upper limit" of data, and any data lying outside these defined bounds can be considered an outlier. The fences provide a guideline by which to define an [[outlier]], which may be defined in other ways. The fences define a "range" outside which an outlier exists; a way to picture this is a boundary of a fence. It is common for the lower and upper fences along with the outliers to be represented by a [[Box plot|boxplot]]. For the boxplot shown on the right, only the vertical heights correspond to the visualized data set while horizontal width of the box is irrelevant. Outliers located outside the fences in a boxplot can be marked as any choice of symbol, such as an "x" or "o". The fences are sometimes also referred to as "whiskers" while the entire plot visual is called a "box-and-whisker" plot. |
The lower fence is the "lower limit" and the upper fence is the "upper limit" of data, and any data lying outside these defined bounds can be considered an outlier. The fences provide a guideline by which to define an [[outlier]], which may be defined in other ways. The fences define a "range" outside which an outlier exists; a way to picture this is a boundary of a fence, outside which are "outsiders" as opposed to outliers. It is common for the lower and upper fences along with the outliers to be represented by a [[Box plot|boxplot]]. For the boxplot shown on the right, only the vertical heights correspond to the visualized data set while horizontal width of the box is irrelevant. Outliers located outside the fences in a boxplot can be marked as any choice of symbol, such as an "x" or "o". The fences are sometimes also referred to as "whiskers" while the entire plot visual is called a "box-and-whisker" plot. |
||
When spotting an outlier in the data set by calculating the interquartile ranges and boxplot features, it might be |
When spotting an outlier in the data set by calculating the interquartile ranges and boxplot features, it might be simple to mistakenly view it as evidence that the population is non-normal or that the sample is contaminated. However, this method should not take place of a [[hypothesis test]] for determining normality of the population. The significance of the outliers vary depending on the sample size. If the sample is small, then it is more probable to get interquartile ranges that are unrepresentatively small, leading to narrower fences. Therefore, it would be more likely to find data that are marked as outliers.<ref>{{Cite journal|last=Dawson|first=Robert|date=July 1, 2011|title=How Significant is a Boxplot Outlier?|journal=Journal of Statistics Education|volume=19|issue=2|doi=10.1080/10691898.2011.11889610|doi-access=free}}</ref> |
||
== Computer software for quartiles == |
== Computer software for quartiles == |
||
Line 194: | Line 194: | ||
|} |
|} |
||
Excel: |
|||
The Excel function ''QUARTILE(array, quart)'' provides the desired quartile value for a given array of data, using Method 3 from above. In the '' |
The Excel function ''QUARTILE(array, quart)'' provides the desired quartile value for a given array of data, using Method 3 from above. In the ''Quartile'' function, array is the dataset of numbers that is being analyzed and quart is any of the following 5 values depending on which quartile is being calculated. <ref>{{Cite web|url=https://exceljet.net/excel-functions/excel-quartile-function|title=How to use the Excel QUARTILE function {{!}} Exceljet|website=exceljet.net|access-date=December 11, 2019}}</ref> |
||
{| class="wikitable" |
{| class="wikitable" |
||
|+ |
|+ |
||
Line 216: | Line 217: | ||
|Maximum value |
|Maximum value |
||
|} |
|} |
||
⚫ | |||
⚫ | In order to calculate quartiles in Matlab, the function ''quantile(A,p)'' can be used. Where A is the vector of data being analyzed and p is the percentage that relates to the quartiles as stated below. <ref>{{Cite web|url=https://www.mathworks.com/help/stats/quantile.html|title=Quantiles of a data set – MATLAB quantile|website=www.mathworks.com|access-date=December 11, 2019}}</ref> |
||
⚫ | |||
⚫ | In order to calculate quartiles in Matlab, the function ''quantile |
||
{| class="wikitable" |
{| class="wikitable" |
||
|+ |
|+ |