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Stats Day 18
Standard deviation as
comparison
SILENT DO NOW
ON DESK:
Chapter 5 Study Guide
DO NOW:
ACT Half Sheet
Check HW with a partner
Homework:
Notes on Chapter 6 p.103-117
Practice Quiz
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Practice Quiz
QUIZ
Calculator
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Find the SD and the Mean for the Data
Sets. Also create a boxplot:
1) 1, 3, 4, 5, 6, 6, 7, 9, 10, 12, 12, 13,
14, 15, 15, 18, 20
2) 88, 90, 95, 98, 65, 75, 78, 80, 52,
99, 96, 93, 85, 80
Here are Dot-Plots of the
grades in each class:
Mean
So, we need to come up with some
way of measuring not just the
average, but also the spread of the
distribution of our data.
Why not just give an average and
the range of data (the highest and
lowest values) to describe the
distribution of the data?
Well, for example, lets say
from a set of data, the
average is 17.95 and the
range is 23.
But what if the data
looked like this:
Here is the average
And here is the range
But really, most of the
numbers are in this
area, and are not
evenly distributed
throughout the range.
Numerical Measure
of Spread
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Spread is important in analysis of data, and we
need an objective (numerical) and specific
measurement:
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STANDARD DEVIATION
HOW MUCH DOES THE DATA DEVIATE (go away from) FROM
THE CENTER (the mean)?
NOTE: IF THE MEAN IS NOT A GOOD MEASURE OF CENTER,
THEN THE STANDARD DEVIATION IS NOT A GOOD MEASURE
OF SPREAD
If the Standard Deviation islarge,
large, it
means the numbers are spread out
from their mean.
If the Standard Deviation is small,
small, it
means the numbers are close to
their mean.
Tomorrow we will talk about
how we can use SD to
compare two sets of data!
Mean
Stats Day 19
Standard deviation as
comparison
SILENT DO NOW
ON DESK:
Chapter 6 Notes
DO NOW:
ACT Half Sheet
Homework DUE WEDNESDAY:
Chapter 6 #5-10
Objective
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SWBAT define z-score
SWBAT calculate the z-score and use
it as a comparison for two different
data distributions
Here is what we
know so far…
Statistics vs Data
• Categorical vs Quantitative Data
• Displaying Categorical Data
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Frequency tables, relative frequency, contingency tables
• Marginal and conditional distribution
Pie charts, bar graphs, segmented bar charts
Displaying Quantitative Data
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Dot plots, stem and leaf, histograms
Describing Quantitative Data: SOCS
• Boxplots (5# summary)
• Standard Deviation!
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Agenda
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Comparing different data sets using
the Standard Deviation
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Z-Score
Practice games
Who did better?
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Allan and Breanna are both doing their homework,
studying, and doing super well in class:
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Allan scored a 90 on the first quiz when the
class average was an 82.
Breanna scored a 90 on this last quiz when
the class average was a 77.
Who would you argue did better?
Why?
Would the spread
matter?
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What if we had this data:
Leslie scored a 90 on a quiz. The average was
an 80. The data was as follows:
65, 68, 68, 68, 70, 88, 90, 90, 95, 98
Paola scored a 90 on a quiz. The average was
an 80. The data was as follows:
70, 78, 78, 78, 80, 80, 82, 82, 82, 90
Who did better? Why?
Using Standard Deviation
as a Comparative Tool
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We are comparing two different data sets
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We are comparing apples to oranges! How do we do that?
We need to take BOTH average and SD
into consideration
• The
standardized value: z-score
Z Score
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The z-score tells us how many
standard deviations we are
from the mean, the avg.
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Let’s go back to our example…
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Leslie scored a 90 on a quiz. The average
was an 80. The data was as follows:
Calculate the zscore for each and
65, 68, 68, 68, 70, 88, 90, 90, 95, 98
compare Leslie’s
score to Paola’s
Paola scored a 90 on a quiz. The average
was an 80. The data was as follows:
70, 78, 78, 78, 80, 80, 82, 82, 82, 90
Another Example
Below are the results from 3 athletes in a three-event track competition.
Decide who receives the gold medal based on the following results:
Event
Competitor
100 m dash
Shot Put
Long Jump
A
10.1 sec
66’
26’
B
9.9 sec
60’
27’
C
10.3 sec
63’
27’3’’
Mean
10 sec
60’
26’
Standard
Deviation
0.2 sec
3’
6’’
Practice Sheet
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Groups of 4
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Compare using Z-Scores
Practice Game
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TRASHKETBALL!
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Groups of 4
Everyone, individually, produces their own work
The whole group tries to get it right first
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Everyone in the group must have the right answer with
work
If one person is right, they can help the others in the
group once finished with work
If whole team gets it right, each person gets a
shot
Question 1
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A normal distribution of scores has a
standard deviation of 10. Find the zscore for a score of 60 when the
mean is 45.
Question 2
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A normal distribution of scores has a
standard deviation of 8. Find the zscore for a score of 59 when the
mean is 43.
Question 3
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The mean speed of vehicles along a
stretch of highway is 56 mph with a
standard deviation of 4 mph. You
measure the speed of three cars
traveling along this stretch of highways
as 62 mph, 47 mph, and 56 mph.
Determine how many SDs each car is
away from the mean. (Find the z-score
that corresponds to each speed.)
Question 4
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A certain brand of automobile tire
has a mean life span of 35,000 miles
and a standard deviation of 2250
miles. If the life spans of three
randomly selected tires are 34,000
miles, 37,000 miles, and 31,000
miles. Find the z-scores that
correspond with each of these
mileages.
Question 5
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A highly selective university will only
admit students who place at least 2zcores above the mean on the ACT
that has a mean of 18 and a
standard deviation of 6. What is the
minimum score that an applicant
must obtain to be admitted to the
university?
Question 6
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The average for the statistics exam
was 75 and the standard deviation
was 8. Andrey was told by the
instructor that he scored 1.5 SDs
below the mean. What was Andrey’s
score?
Question 7
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The monthly utility bills in Chicago have
a mean of $70 and a standard deviation
of $8. The monthly utility bills in Boston
have a mean of $64 and a standard
deviation of $10.
If I pay $79 on utilities in Chicago and I
paid $75 when I was in Boston. In
which city did I find the better deal?
Homework
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Ch. 6 #5-10