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Z-Score 1

The document discusses z-scores, which are used to standardize data points from a normally distributed data set by reflecting how many standard deviations above or below the mean a data value is. It provides the formula for calculating z-scores and works through examples of finding z-scores based on given means, standard deviations, and data values. The examples analyze test score and gas mileage data to determine z-scores and compare relative performance.

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385 views10 pages

Z-Score 1

The document discusses z-scores, which are used to standardize data points from a normally distributed data set by reflecting how many standard deviations above or below the mean a data value is. It provides the formula for calculating z-scores and works through examples of finding z-scores based on given means, standard deviations, and data values. The examples analyze test score and gas mileage data to determine z-scores and compare relative performance.

Uploaded by

api-276566085
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPT, PDF, TXT or read online on Scribd
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Objectives

The student will be able to:


find the z-scores of a data set

Z-scores
Copy/Complete on Notes
Handout
A z-score is used to standardize data points
from a normally distributed data set. A z-score
reflects how many standard deviations above or
below the mean a data value is from the mean.

The z-score is positive if the data


value lies above the mean and
negative if the data value lies
below the mean.

z-score formula
(copy onto notes handout)
x
z

Where x represents an element


of the data set, the mean is
represented by and
standard deviation by the
Greek symbol (sigma)

#2 on Handout
Analyzing the data
Suppose SAT scores among college
students are normally distributed with
a mean of 500 and a standard deviation
of 100. If a student scores a 700, what
would be her z-score?

AnswerNow

#2 on Handout
Analyzing the data
Suppose SAT scores among college students
are normally distributed with a mean of 500
and a standard deviation of 100. If a student
scores a 700, what would be her z-score?

700 500
z
2
100

Her z-score would be 2 which


means her score is two standard
deviations above the mean.

#3 on Handout
Analyzing the data
A. A set of math test scores has a mean
of 70 and a standard deviation of 8.
B. A set of English test scores has a
mean of 74 and a standard deviation of
16.

For which test would a score of 78


have a higher standing?
AnswerNow

#3 on Handout
Analyzing the data

A set of math test scores has a mean of 70 and a standard


deviation of 8.
A set of English test scores has a mean of 74 and a standard
deviation of 16.
For which test would a score of 78 have a higher standing?

To solve: Find the z-score for each test.


78-70
math z -score =
1
8 English z -score= 78-74 .25
16
The math score would have the highest
standing since it is 1 standard deviation above
the mean while the English score is only .25
standard deviation above the mean.

Analyzing the data

What will be the miles per gallon for


a Toyota Camry when the average
mpg is 23, it has a z value of 1.5 and
a standard deviation of 2?

AnswerNow

Analyzing the data


What will be the miles per gallon for a Toyota
Camry when the average mpg is 23, it has a
z value of 1.5 and a standard deviation of 2?

x
Using the formula for z-scores: z

x 23
1.5
2

3 x 23 x 26

The Toyota Camry would be expected


to use 26 mpg of gasoline.

Think Pair Share Practice


Z-Scores

#1 on the Handout

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