Name:
Ms. D’Amato
Date:
Block:
Z-Scores
Let’s review our measures of spread…….
From 1984 to 1995, the winning scores for a golf tournament were 280, 282, 285, 272, 279, and
278. Find the range, absolute mean deviation, and standard deviation.
Range →
Mean Absolute Deviation →
FORMULA: ____________________________
𝒙𝒊
n= _________
|𝒙𝒊 − 𝝁|
𝒙𝒊 − 𝝁
∑=
Standard Deviation → σ: _______________
What is the formula for Standard Deviation?
Quick Review of Standard Deviation:
You just found the mean and standard deviation of a particular data set. The mean is 10 and
the standard deviation is 4.
µ = 10; σ = 4
1.) How many standard deviations away from the mean is 14?
2.) How many standard deviations away from the mean is 6?
3.) How many standard deviations away from the mean is 2?
4.) How many standard deviations away from the mean is 12?
Z-Score: used to determine how many standard deviations units a term is above or below the
mean



Has a __________________ value if the element lies above the mean.
Has a __________________ value if the element lies below the mean.
Measures in terms of standard deviation units.
FORMULA FOR Z-score: z =
xi  

EXAMPLE 1: Calculating the Z-Score of a data point
If we have a data set where µ = 8 and σ = 2, find the Z-Score for the following data points.
a.) x = 12
b.) x = 6
c.) x = 7
EXAMPLE 2: Calculating the Z-Score of a data point.
If we have a data set where µ = 200 and σ = 10, find the Z-Score for the following data points.
a.)
x = 180
b.) x = 215
c.) x = 230
Why Do We Find The Z-Score?
A way to compare apples and oranges!
EXAMPLE 3: Comparing Apples to Oranges Which One is Larger?
The average apple has a diameter of 3.25 inches with a standard deviation of .5 inch. The
average orange has a diameter of 4.5 inches and has a standard deviation of 1 inch. If I have an
apple with a diameter of 4 inches and an orange with a diameter of 5.5 inches, which fruit is
largest compared to others of its kind?
APPLES
ORANGES
μ: _____________
μ: _____________
σ: _____________
σ: _____________
xi :____________
xi :____________
Work with Formula:
Work with Formula:
EXAMPLE 4: Test Scores
In English class, Tori took a test on Of Mice and Men and another test on Shakespeare.
Tori wants to find out which test she did better on in comparison to her classmates. Tori’s
teacher told her that the average score for the Of Mice and Men Test was a 78 with a
standard deviation of 8, and the average score of the Shakespeare test was an 86 with a
standard deviation of 3. If Tori earned a 90 on her Of Mice and Men test and a 92 on her
Shakespeare test, on which test did she do best?
OF MICE AND MEN
SHAKESPEARE
μ: _____________
μ: _____________
σ: _____________
σ: _____________
xi :____________
xi :____________
Work with Formula:
Work with Formula:
Steven got a 72 on his Of Mice and Men tests and an 88 on his Shakespeare test. Which
test did he do better on?
OF MICE AND MEN
SHAKESPEARE
μ: _____________
μ: _____________
σ: _____________
σ: _____________
xi :____________
xi :____________
Work with Formula:
Work with Formula: