2.1 – Describing Location in a
Distribution
Day 1 on Assignment Guide
Percentiles
• The percent of observations in a set of data
that are below a certain value.
• It is possible to include equal to, but we will strictly do below
for consistency
Cumulative Relative Frequency Plot
• Remember relative frequency is percent
• Cumulative – running total
AKA “Ogives”
Shape for Cumulative Relative
Frequency Plot
Where is the graph the
steepest?
What does this mean?
Sketch a Cumulative
Relative Frequency Plot for
this data. Describe the
shape.
Sketch a Cumulative
Relative Frequency Plot for
symmetric and skewed left
Check Your Understanding
Turn to page 89 and do problems 1 – 4
We will do one at a time on the whiteboards
z-scores
• Also called standardized value
• It is unit-less
• Tells us how many standard deviations away
from the mean a particular value is
• Formula is on your formula sheet and on p. 90
In 2009, the mean number of wins in MLB
was 81 with a standard deviation of 11.4 wins.
1. Find and interpret the z-score for the NY
Yankees if they had 103 wins.
2. Find and interpret the z-score for the NY
Mets if they had 70 wins.
1. z-score = (103-81)/11.4 = 1.93.
Interpret: The NY Yankees were 1.93
standard deviations above the mean
number of wins.
2. z-score = (70-81)/11.4 = -0.96.
Interpret: The NY Mets were 0.96
standard deviations below the mean
number of wins.