#
Section 11-4

#
Box & Whisker Plots

To understand
box-and-whisker plots
, you have to understand
medians
and
quartiles
of a data set.

The median is the middle number of a set of data, or the average of the two middle numbers (if there are an even number of data points).

The median (Q
_{
2
}
) divides the data set into two parts, the upper set and the lower set. The
**
lower quartile
**
(Q
_{
1
}
) is the median of the lower half, and the
**
upper quartile
**
(Q
_{
3
}
) is the median of the upper half.

Example:

Find Q
_{
1
}
, Q
_{
2
}
, and Q
_{
3
}
for the following data set:

2, 6, 7, 8, 8, 11, 12, 13, 14, 15, 22, 23

There are 12 data points. The middle two are 11 and 12. So the median, Q
_{
2
}
, is 11.5.

The "lower half" of the data set is the set {2, 6, 7, 8, 8, 11}. The median here is 7.5. So Q
_{
1
}
= 7.5.

The "upper half" of the data set is the set {12, 13, 14, 15, 22, 23}. The median here is 14.5. So Q
_{
3
}
= 14.5.

A box-and-whisker plot displays the values Q
_{
1
}
, Q
_{
2
}
, and Q
_{
3
}
, along with the extreme values of the data set (2 and 23, in this case):

A box & whisker plot shows a "box" with left edge at Q
_{
1
}
, right edge at Q
_{
3
}
, the "middle" of the box at Q
_{
2
}
(the median) and the maximum and minimum as "whiskers".