Secondly, the median is that line that is placed vertically at the centre of the box in a manner that splits the box into two.The interquartile interval is covered by the box, where 50% of the data is present. The left and right sides of the box are the regions that mark the lower as well as the upper quartiles.It can be clearly seen in the above diagram that – Let us now understand each representation in this diagram of the box and whisker plot. The following is the diagrammatic representation of a box and whisker plot. Let us now understand the description of a box and a whisker plot. Minimum – It is the lowest value in a given dataset.Maximum – It is the highest value in a given dataset.Outliers – If a data value is very far away from the quartiles (either much less than Q1 or much greater than Q3 ), it is termed as an outlier.They are used to indicate variability out of the upper and lower quartiles. Whiskers – These are the lines that extend from the boxes.Interquartile range – it ranges from the 25th to the 75th percentile.Third quartile – It is the middle value between the median and the highest value of the dataset.First quartile – It is the middle number between the smallest number and the median of the dataset.Median – The middle value of the dataset.Some important terms relevant for obtaining these five numbers are – In other words, Box and Whisker Plots are a standardized way of displaying the distribution of data based on a five-number summary (minimum, first quartile (Q1), median, third quartile (Q3), and “maximum”). These five numbers are median, upper and lower quartile, minimum and maximum data values which are also known as extremes. The box and whisker plot, which is also known as simply the box plot, is a type of graph that helps visualize the five-number summary. Now that we have recalled what is meant by median and quartile, let us learn what we mean by box and whisker plots. A particular quartile is a border between two neighbouring quarters of the distribution. Quartiles – A Quartile is a percentile measure that divides the total of 100% into four equal parts: 25%,50%,75% and 100%. If n is odd, then use the following formula – Median – The median of a group of observations is the value of the variable which divides the group of n numbers into two equal parts. Now before we move further and learn more about the box and whisker plots, we must first recall some important terms that are relevant to the understanding of the box and whisker plots. Tukey also considered an additional variation in which the outliers are indicated separately and whiskers are dashed, ending with dashed crossbars at “adjacent values”. He used extended the whiskers all the way to the extreme data points and drew an unfilled dot at the maximum along with a hatched horizontal strip at the minimum.

For instance, Tukey’s original formulation did not have horizontal crossbars. However, the arrangement of the box and whisker that is in use today slightly varies from what was proposed by J Turkey. Using Box and Whisker Plots for Comparative AnalysisĪ box-and-whisker plot is a histogram like method of displaying data.Advantages of using Box and Whisker plots.'Box-and-Whisker Plot.'įrom MathWorld-A Wolfram Web Resource. On Wolfram|Alpha Box-and-Whisker Plot Cite this as: 'Box-and-Whisker Plots.' §2C in Exploratoryĭata Analysis. 'Box Plot.' §1.3.3.7 in NIST/ SEMATECH e-Handbook of Statistical (values closest to but still inside the inner fences). In which the outliers are indicated separately and whiskers are dashed, ending with Tukey also considered an additional variation

Out to some arbitrary minimum and maximum values and identifying the outliers withĮxplicit labels (Tukey 1977, p. 41). In addition, Tukey's original formulation lacked horizontal crossbars,Įxtended the whiskers all the way to the extreme data points, and drew an unfilledĭot at the maximum and a hatched horizontal strip at the minimum, as illustratedĪbove (left figure Tukey 1977, p. 40).

In Tukey's original definition, the closely-related and lesser known hinges and were used instead Box-and-whisker plots areĪ number of other slightly different conventions are sometimes used. Them side by side (Gonick and Smith 1993, p. 21). Now extend the 'whiskers' to the farthest points thatĪre not outliers (i.e., that are within 3/2 times the interquartileĮvery point more than 3/2 times the interquartile Draw the statistical median as a horizontal Plot, draw a box with ends at the quartiles and. A box-and-whisker plot (sometimes called simply a box plot) is a histogram-like method of displaying data, invented by J. Tukey.

How to draw box and whisker plot