Editing Box plot (section)

=== Example without outliers ===
[[File:No Outlier.png|thumb|Figure 5. The generated boxplot figure of the example on the left with no outliers]]
A series of hourly temperatures were measured throughout the day in degrees Fahrenheit. The recorded values are listed in order as follows (°F): 57, 57, 57, 58, 63, 66, 66, 67, 67, 68, 69, 70, 70, 70, 70, 72, 73, 75, 75, 76, 76, 78, 79, 81.

A box plot of the data set can be generated by first calculating five relevant values of this data set: minimum, maximum, median ('''''Q''<sub>2</sub>'''), first quartile ('''''Q''<sub>1</sub>'''), and third quartile ('''''Q''<sub>3</sub>''').

The minimum is the smallest number of the data set. In this case, the minimum recorded day temperature is 57°F.

The maximum is the largest number of the data set. In this case, the maximum recorded day temperature is 81°F.

The median is the "middle" number of the ordered data set. This means that exactly 50% of the elements are below the median and 50% of the elements are greater than the median. The median of this ordered data set is 70°F.

The first quartile value ('''''Q''<sub>1</sub>''' '''or 25th percentile)''' is the number that marks one quarter of the ordered data set. In other words, there are exactly 25% of the elements that are less than the first quartile and exactly 75% of the elements that are greater than it. The first quartile value can be easily determined by finding the "middle" number between the minimum and the median. For the hourly temperatures, the "middle" number found between 57°F and 70°F is 66°F.

The third quartile value ('''''Q''<sub>3</sub>''' '''or 75th percentile)''' is the number that marks three quarters of the ordered data set. In other words, there are exactly 75% of the elements that are less than the third quartile and 25% of the elements that are greater than it. The third quartile value can be easily obtained by finding the "middle" number between the median and the maximum. For the hourly temperatures, the "middle" number between 70°F and 81°F is 75°F.

The interquartile range, or IQR, can be calculated by subtracting the first quartile value ('''''Q''<sub>1</sub>''') from the third quartile value ('''''Q''<sub>3</sub>'''):

: <math>\text{IQR} = Q_3 - Q_1=75^\circ F-66^\circ F=9^\circ F.</math>

Hence, <math>1.5  \text{IQR}=1.5 \cdot 9^\circ F=13.5 ^\circ F.</math>

1.5 IQR above the third quartile is:

: <math>Q_3+1.5\text{ IQR}=75^\circ F+13.5^\circ F=88.5^\circ F.</math>

1.5 IQR below the first quartile is:

: <math>Q_1-1.5\text{ IQR}=66^\circ F-13.5^\circ F=52.5^\circ F.</math>

The upper whisker boundary of the box-plot is the largest data value that is within 1.5 IQR above the third quartile. Here, 1.5 IQR above the third quartile is 88.5°F and the maximum is 81°F. Therefore, the upper whisker is drawn at the value of the maximum, which is 81°F.

Similarly, the lower whisker boundary of the box plot is the smallest data value that is within 1.5 IQR below the first quartile. Here, 1.5 IQR below the first quartile is 52.5°F and the minimum is 57°F. Therefore, the lower whisker is drawn at the value of the minimum, which is 57°F.