http://www.ck12.org Chapter 7. Organizing and Displaying Data
Guidance
In traditional statistics, data is organized by using a frequency distribution. The results of the frequency distribution
can then be used to create various graphs, such as a histogram or a frequency polygon, which indicate the shape
or nature of the distribution. The shape of the distribution will allow you to confirm various conjectures about the
nature of the data.
To examine data in order to identify patterns, trends, or relationships, exploratory data analysis is used. In exploratory
data analysis, organized data is displayed in order to make decisions or suggestions regarding further actions. Abox-
and-whisker plot(often called a box plot) can be used to graphically represent the data set, and the graph involves
plotting 5 specific values. The 5 specific values are often referred to as afive-number summaryof the organized
data set. The five-number summary consists of the following:
- The lowest number in the data set (minimum value)
- The median of the lower quartile:Q 1 (median of the first half of the data set)
- The median of the entire data set (median)
- The median of the upper quartile:Q 3 (median of the second half of the data set)
- The highest number in the data set (maximum value)
The display of the five-number summary produces a box-and-whisker plot as shown below:
The above model of a box-and-whisker plot shows 2 horizontal lines (the whiskers) that each contain 25% of the
data and are of the same length. In addition, it shows that the median of the data set is in the middle of the box,
which contains 50% of the data. The lengths of the whiskers and the location of the median with respect to the center
of the box are used to describe the distribution of the data. It’s important to note that this is just an example. Not all
box-and-whisker plots have the median in the middle of the box and whiskers of the same size.
Information about the data set that can be determined from the box-and-whisker plot with respect to the location of
the median includes the following:
a. If the median is located in the center or near the center of the box, the distribution is approximately symmetric.
b. If the median is located to the left of the center of the box, the distribution is positively skewed.
c. If the median is located to the right of the center of the box, the distribution is negatively skewed.