2.6 Measure of Relative Standing
z – scores.
the number of standard deviations that a given value x is above or below
mean. It is found using the following expressions:
Sample
z
xx
s
the
Population
z
x

Round z to two decimal places.
Comparing Heights.
NBA superstar Michael Jordan is 78 in. tall and WNBA basketball player Rebecca Lobo
is 76 in. tall. Jordan is obviously taller by 2 in., but which player is relatively taller? Does
Jordan’s height among men exceed Lobo’s height among women? Men have heights with
a mean of 69.0 in and a standard deviation of 2.8 in.; women have heights with a mean of
63.6 in. and a standard deviation of 2.5 in.(based on data from the National Health
Survey)
Calculate the z-scores.
Jordan:
Lobo:
FIGURE 2-14
Are Michael Jordan and Rebecca Lobo unusually tall? _____________
Calculate the z-score for Mugsy Bogues. Mugsy is 63 in. tall.
Is Mugsy’s height an unusual value? _____________
If an IQ test has a mean of 100 and a standard deviation of 15, find the
corresponding z score for each IQ.
a.
b.
c.
d.
e.
115
122
93
100
85
Quartiles and Percents.
 Q1 (First Quartile) separates the bottom 25% of sorted values from the top
75%.
 Q2 (Second Quartile) same as the median; separates the bottom 50% of
sorted values from the top 50%.
 Q3 (Third Quartile) separates the bottom 75% of sorted values from the top
25%.
Q1, Q2, Q3
divides ranked scores into four equal parts
25%
(minimum)
25%
25% 25%
Q1 Q2 Q3
(maximum)
(median)
Just as there are three quartiles separating data set into four parts, there are also 99
percentiles, denoted P1,P2,…., P99.
To find a percentile that corresponds to a particular value x use:
Percentile of value x =
number of values less than x
total number of values
Cotinine levels of smokers.
Find the percentile corresponding to the cotinine level of 112.
Find the percentile corresponding to the following values in the same table.
a. 198
b. 266
c. 35
Homework: 2-6 , 1-11 odd, 13-16
• 100