Also, the Outlier Multiplier is not fixed at 1.5 but can be set to another value by the user (in the dialog box for the Descriptive Statistics and Normality data analysis tool). The output for Example 1 of Creating Box Plots in Excel is shown in Figure 3.įigure 3 – Output from Box Plots with Outliers toolĪs you can see, the output is similar to that shown in Figure 1, except that this version is available in other releases of Excel prior to Excel 2016. To produce such a box plot, proceed as in Example 1 of Creating Box Plots in Excel, except that this time you should select the Box Plots with Outliers option of the Descriptive Statistics and Normality data analysis tool. The Real Statistics Resource Pack also provides a way of generating box plots with outliers. In fact, since the Excel Box Plot is only available in Excel 2016, we can also use the Excel 2016 (non-array) formulas =MAXIFS(C2:C11,”=”&H8). Note that we could also use the array formula
The only outlier is the value 1850 for Brand B, which is higher than the upper whisker, and so is shown as a dot. The boundaries of the box and whiskers are as calculated by the values and formulas shown in Figure 2. Values outside this range are considered to be outliers and are represented by dots. The whiskers extend up from the top of the box to the largest data element that is less than or equal to 1.5 times the interquartile range (IQR) and down from the bottom of the box to the smallest data element that is larger than 1.5 times the IQR. The box part of the chart is as described above, except that the mean is shown as an ×. You can add a legend as well as chart and axis titles as usual. The chart shown on the right side of Figure 1 will appear.įigure 1 – Excel’s Box and Whiskers chart
To access this capability for Example 1 of Creating Box Plots in Excel, highlight the data range A2:C11 (from Figure 1) and select Insert > Charts|Statistical > Box and Whiskers. Here, 1.5 IQR above the third quartile is 88.5 ☏ and the maximum is 81 ☏.Starting with Excel 2016 Microsoft added a Box and Whiskers chart capability. The upper whisker boundary of the box-plot is the largest data value that is within 1.5 IQR above the third quartile.
Interquartile range (IQR) : the distance between the upper and lower quartiles. In addition to the minimum and maximum values used to construct a box-plot, another important element that can also be employed to obtain a box-plot is the interquartile range (IQR), as denoted below: Third quartile ( Q 3 or 75th percentile): also known as the upper quartile q n(0.75), it is the median of the upper half of the dataset. First quartile ( Q 1 or 25th percentile): also known as the lower quartile q n(0.25), it is the median of the lower half of the dataset. Median ( Q 2 or 50th percentile): the middle value in the data set. Maximum ( Q 4 or 100th percentile): the highest data point in the data set excluding any outliers. Minimum ( Q 0 or 0th percentile): the lowest data point in the data set excluding any outliers. Same box-plot with whiskers drawn within the 1.5 IQR valueĪ boxplot is a standardized way of displaying the dataset based on the five-number summary: the minimum, the maximum, the sample median, and the first and third quartiles. Box plots can be drawn either horizontally or vertically.įigure 3. In addition, the box-plot allows one to visually estimate various L-estimators, notably the interquartile range, midhinge, range, mid-range, and trimean. The spacings in each subsection of the box-plot indicate the degree of dispersion (spread) and skewness of the data, which are usually described using the five-number summary. Outliers that differ significantly from the rest of the dataset may be plotted as individual points beyond the whiskers on the box-plot.īox plots are non-parametric: they display variation in samples of a statistical population without making any assumptions of the underlying statistical distribution (though Tukey's boxplot assumes symmetry for the whiskers and normality for their length). In addition to the box on a box plot, there can be lines (which are called whiskers) extending from the box indicating variability outside the upper and lower quartiles, thus, the plot is also termed as the box-and-whisker plot and the box-and-whisker diagram. In descriptive statistics, a box plot or boxplot is a method for graphically demonstrating the locality, spread and skewness groups of numerical data through their quartiles. Box plot of data from the Michelson experiment
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