CK-12 Probability and Statistics - Advanced

2.1. Histograms and Frequency Distributions http://www.ck12.org

in the second curve is mound shaped, but the center of the data is concentrated on the left side of the distribution.
The right side of the data is spread out across a wider area. This type of distribution is referred to asskewed right.
Be careful!! Many beginning statistics students think it would intuitively make sense to refer to the side with the
concentration of the data as the direction of the skewing. Instead, it is the direction of the long, spread out section
of data, called thetail,that determines the direction of the skewing. For example, in the 3rdcurve, the left tail of the
distribution is stretched out, so this distribution isskewed left. Our student bottle data has this skewed left shape.

Cumulative Frequency Histograms and Ogive Plots

Very often it is helpful to know how much of the data accumulates over the range of the distribution. To do this, we
will add to our frequency table by including thecumulative frequency,which is how many of the data points are in
all the classesup to and includingthat class.

TABLE2.7:

Number of Plastic Beverage Bottles

per Week

Frequency Cumulative Frequency

1 1 1

2 1 2

3 3 5

4 4 9

5 6 15

6 8 23

7 7 30

8 2 32

Figure:Cumulative Frequency Table for Bottle Data

For example, the cumulative frequency for 5 bottles per week is 15 because 15 students consumed 5or fewerbottles
per week. Notice that the cumulative frequency for the last class is the same as the total number of students in the
data. This should always be the case.

If we drew a histogram of the cumulative frequencies, or acumulative frequency histogram,it would look as
follows: