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Box-and-Whisker Plots

Making a Box-and-Whisker Plot

Step 1: Arrange the values in increasing order and compute [pic].

Step 2: Draw a number line that includes the minimum and maximum values.

Step 3: Make a box whose left end is at [pic] and whose right end is at [pic].

Step 4: Draw vertical line segment to divide the box at, [pic], the median.

Step 5: Draw a line segment from [pic] to the minimum value and another line segment from [pic] to the maximum value for the left and right whiskers.

A box-and-whisker plot displays how the values of the data are distributed.

Outliers

Outliers-are unusual data. A data value that is less than [pic] or greater than [pic].

Quartiles

First Quartile - median of the lower half of the data set

Second Quartile -median of the data set.

Third Quartile- median of the upper half of the data set

Interquartile range- [pic]

Example:

The number of calls received by a crisis hotline during 17 randomly selected is given below

|50 |57 |77 |66 |53 |72 |

|51 |88 |82 |70 |112 |107 |

|69 |88 |98 |65 |155 | |

Median is 72

The median of the lower half [pic] = 61

The median of the upper half [pic]

IQR = 93 – 61 = 32

Find any possible outliers below [pic]

[pic]

Find any possible outliers above [pic]

[pic]

There are no values less than or equal to 13. Because the data value 155 is greater than 141, 155 is a possible outlier.

You can use box-and-whisker plots to compare the distribution of two set of similar data, such as the monthly mean temperatures for two cities.

Monthly mean temperatures for Los Angles and Chicago (1961 – 1990)

|Months |Los Angeles...