Question

How do you create box and whisker plots on a graphing calculator?

Answer 1

Hint: For solving this particular question, that is to create a box and whisker, we have to follow certain steps where we have to find five points namely the minimum value, the maximum value, and the three quartiles.

Complete step by step solution:
Let us Suppose that we have the following set of data:
$\{ 5.1,4.8,4.2,4.7,4.5,5.2,4.9,4.6,3.9,4.4,4.1,4.0,4.7,4.5,4.2,4.6,4.3\} $
Now for creating box and whisker plots we have to follow certain steps, given below.
1) The very first step for creating a box-and-whisker plot is by arranging your data set in a particular order that is in ascending order:
 \[\left\{ {3.9,4.0,4.1,4.2,4.2,4.3,4.4,4.5,4.5,4.6,4.6,4.7,4.7,4.8,4.9,5.1,5.2} \right\}\]
2) Now, the second step, we have to find the median of the given set , as we know that we have $17$ values in the given data set, the median will be at 9th position, that is \[4.5\] . Now this median value considered as the second quartile point :
 \[{Q_2} = 4.5\]
3) The third step is to find the other two quartile points , ${Q_1}$ and ${Q_3}$, we can find it by finding the median values of the two data subsets separated by the second quartile point that is \[{Q_2}\] .
We have the first subset \[\left\{ {3.9,4.0,4.1,4.2,4.2,4.3,4.4,4.5} \right\}\] , here we have $8$ values, so its median is given by the arithmetic mean of the middle values: \[{Q_1} = \dfrac{{4.2 + 4.2}}{2} = 4.2\]
We have the second subset \[\left\{ {4.6,4.6,4.7,4.7,4.8,4.9,5.1,5.2} \right\}\] , here we have $8$ values again, so its median is given by the arithmetic mean of the middle values: \[{Q_3} = \dfrac{{4.7 + 4.8}}{2} = 4.75\]
4) Now, in the fourth step, we will mark the five significant values on a scale:
the minimum and the maximum values from the given data set: \[3.9\] and \[5.2\]
the quartiles which we already calculated \[{Q_1},{Q_2}\] and \[{Q_3}:{\text{ }}4.2,4.5\] and \[4.75\]
5) The fifth step is to draw the box, which goes from \[{Q_1}\] to \[{Q_3}\] , that is from the values \[4.2\] to \[4.75\]
6) The last sixth step is to draw the whiskers at the endpoints that are the minimum and maximum values that are \[3.9\] and \[5.2\] .

Note: If we have questions similar in nature as that of above can be approached in a similar manner and we can solve it easily by following the given step properly. While calculating the median of the given set you have to arrange the given data in the proper order.