Download Vectors and Their Applications


By the end of this section, you should be
able to:
› Find and interpret the percentile of an individual
value within a distribution of data.
› Estimate percentiles and individual values using
a cumulative relative frequency graph.
› Find and interpret the standardized score (zscore) of an individual value within a distribution
of data.
› Describe the effect of adding, subtracting,
multiplying by, or dividing by a constant on the
shape, center, and spread of a distribution of
data.

Take the heights of each student (in
inches) and place them on a number
line from 58 inches to 78 inches.

Make a dot plot.

What percent of the students have a
height less than yours? (This is percentile.)

With a partner, find the mean and
standard deviation of the class heights.

Is your height above or below the
mean?

How many standard deviations is it from
the mean? (This is your z-score.)

What would happen if we converted the
height to centimeters? (1 inch = 2.54
centimeters.)

How would the unit change affect
measures of center, spread, and
location (percentile and z-score) that
you calculated?

Definition: The percentage of
observations less than a specific data
point.

Here are the scores of 12 exams taken in
a class. The bold score is Jenny’s.

79, 81, 77, 74, 86, 90, 79, 93, 75, 80, 67, 72.

Find the percentile Jenny scored in.

What is the relationship between
percentiles and quartiles?

Cumulative relative frequency graphs.

Find the ages of everyone in the class
and record their frequency. (How often
they occur)

Find their relative frequency. (Number of
occurrences / total)

Find their cumulative frequency. (Each
frequency added to previous
frequency.)

Find their cumulative relative frequency.

Create an ogive (cumulative relative
frequency graph).

Extra time? Work on homework!