Data can be displayed in many ways. One method of displaying a set of data is with a boxandwhisker plot.
Boxandwhisker plots:
 are helpful in interpreting the distribution of data.
 are used to summarize data and to illustrate the variability of the data.
 is a pictorial representation of the variability of the data.
 The plots graphically display the median, quartiles, interquartile range and extreme values in a set of data.
 They can be drawn vertically or horizontally.
 It consists of rectangular box with the ends or hinges located at the first and third quartiles.
 The segments extending from the ends of the box are called whiskers.
 The whiskers stop at the extreme values of the set, unless the set contains outliners.
 Outliners are extreme values that are more than 1.5 times the interquartile range beyond the upper and lower quartiles.
 Outliners are represented by single point.
 If an outliner exists, each whisker is extended to the last value of the data that is not an outliner.
 The dimensions of the boxandwhisker plot help characterize the data.
 Each whisker and each small box contains 25% of the data.
 If the whisker or box is short, the data are concentrated over a narrower range of values.
 The longer the whisker or box, the larger the range of the data in that quartile.
If the data is arranged in order and the median is found, the set of data is divided into two groups. If the median of each group is found, the data is divided into two groups. Each of these groups is called a quartile.
Quartiles separate the original set of data into four equal parts. Each of these parts contains onefourth of the data. There are three quartile points Q_{1}, Q_{2}, Q_{3} that denote the breaks in the data for each quartile. The median is the second quartile point Q_{2}.
The medians of the two groups defined by the median are the first quartile points Q_{1} and the third Q_{3}. One fourth of the data is less than the first quartile point Q_{1}, and three fourth of the data is less than the third quartile point Q_{3}.
The difference between the first quartile point and third quartile point is called the interquartile range. When the interquartile range is dived by 2, the quotient is called the semiinterquartile range.
Example:
Math test scores of Mrs B's class are given as: 80, 75, 90, 95, 65, 65, 80, 85, 70, 100. Constructing a boxandwhisker plot for the data.
 Write the data in ascending order and find the first quartile, the median, the third quartile, the smallest value and the largest value.
65, 65, 70, 75,80, 80, 85, 90, 95, 100
median Q_{2} = 80
first quartile Q_{1} = 70
third quartile Q_{3}= 90
smallest value = 65
largest value = 100
 Place a circle beneath each of these values on a number line.
 Draw a box with ends through the points for the first and third quartiles. Then draw a vertical line through the box at the median point. Then, draw the whiskers (or lines) from each end of the box to the smallest and largest values.
Directions: Answer the following questions. Also draw a boxandwhisker plot for the following data set:
4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.7, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4
77, 79, 80, 86, 87, 87, 94, 99
79, 53, 82, 91, 87, 98, 80, 93
