Download Sec. 2.5 – Measures of Position

Sec. 2.5 – Measures of Position
___________ are numbers that partition, or divide, an ordered data set into equal
parts.
The three ___________ ,_______________________, approximately divide an
ordered data set into four equal parts.
__________ is also known as the median.
The test scores of 15 employees enrolled in a CPR training course are listed. Find
the quartiles of the data set.
13
9
18
15
14
21
7
11
20
5
18
37
16
17
10
The ____________________ ____________ (IQR) of a data set is the difference
between the third and first quartiles.
𝐼𝑛𝑡𝑒𝑟𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 𝑟𝑎𝑛𝑔𝑒 (𝐼𝑄𝑅) =
 Note: One way to find outliers is to take the 𝐼𝑄𝑅 ∗ 1.5. Then subtract this
quantity from 𝑄1 and add this quantity to 𝑄3 . Any data point outside this
interval can be considered an outlier.
What is the IQR of the CPR scores? Are there any outliers?
A _______-_______________ ________________ lists the following about the
data set.
1.
2.
3.
What is the five-number summary for the CPR scores?
4.
5.
A ___________-and- _________________ plot is a graphical way of representing
a five-number summary.
Create a box-and-whisker plot of the CPR scores.
In addition to percentiles you can divide data into other fractiles.
Fractiles
Summary
Symbols
Divides a data set into________ equal
parts.
Divides a data set into________ equal
parts.
Divides a data set into________ equal
parts.
 If someone is in the 87th percentile for weight, then it means the person
weighs more than 87% of all individuals in the _____________.
 Note that 25th percentile = _________
75th percentile =__________
50th percentile =_________
You can use the following formula to find the percentile for a data point.
Percentile of 𝑥 =
Looking back at the CPR scores, what percentile corresponds to the score of 18?
What percentile corresponds to the score of 20?
z-score
The ____________ represents the number of standard deviations a given value 𝑥
falls from the mean 𝜇.
The formula for z-score is given below.
𝑧=
z-score example
The mean speed of vehicles along a stretch of highway is 56 miles per hour with a
standard deviation of 4 miles per hour. You measure the speed of three cars
traveling along this stretch of highway as 62 miles per hour, 47 miles per hour,
and 56 miles per hour. Find the z-score that corresponds to each speed. What can
you conclude?
Generally any data point more than two standard deviations away from the mean
is considered unusual. Are any of these speeds in the example above considered
unusual?
Another example
For the statistics test scores in a class the mean is 63 and the standard deviation is
7.0, and for the biology test scores in a different class the mean is 23 and the
standard deviation is 3.9.
A. If a student scored a 73 on the statistics test and a 26 on the biology test, then
for which test did the student have the better score?
B. If a student scored 63 on the statistics test and a 23 on the biology test, then
for which test did the student have a better score?