This means that the whisker reaches the value that is the furthest from the centre while still being inside a distance of 1.5 times the interquartile range from the lower or upper quartile. Moreover, there are two ways of representing the box and the whisker plot – horizontal or vertical manner.Īn important aspect of the box and the whisker plot is that a variation of the box and whisker plot restricts the length of the whiskers to a maximum of 1.5 times the interquartile range. It is important to note here that another characteristic of the box and the whisker plot is the presentation of a graph with an axis that is used for indicating the values. These whiskers can go from the minimum to the lower quartile (which is present at the start of the box) and then it can go from the upper quartile (which is present at the end of the box) to the maximum.
Next, there can be seen two lines that are present outside the box. There are a number of times when the mean is also indicated using a dot or a cross on the box plot. 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.
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