Math 11 Elementary Statistics In Class 3.3 Measures of Position (or location) Name Date Example 1: Computing and interpreting z- Scores A National Center for Health Statistics study states that the mean height for adult men in the United States is u = 69.4 inches, with a standard deviation of o = 3.1 inches. The mean height for adult women is u = 63.8 inches, with a standard deviation of o = 2.8 inches. Who is taller relative to their gender, a man 73 inches tall, or a woman 68 inches tall? Work through this problem in steps: The man's height is X = The men's mean is = The men's standard deviation is The man's z-score is z = (x - p)/o = ( _- So standard deviations from the mean Zman = The woman's height is x = The women's mean is The women's standard deviation is The woman's z-score is z = (x - p)/o = (___- standard deviations from the mean So Zwoman %3D Which one is larger? Example 2: 0.00, 0.08, 0.13, 0.14, 0.16, 0.17, 0.20, 0.29, .056, 0.70, 0.79 L = .25(11) = 2.75 which rounds to 3, so the 3rd number is the 25th percentile and its value is L = .50(11) = 5.5 which rounds to 6, so the 6th number is the 50th percentile, or the median and its value is L = .75(11) = 8.25 which rounds to 9, so the 9th number is the 75th
Math 11 Elementary Statistics In Class 3.3 Measures of Position (or location) Name Date Example 1: Computing and interpreting z- Scores A National Center for Health Statistics study states that the mean height for adult men in the United States is u = 69.4 inches, with a standard deviation of o = 3.1 inches. The mean height for adult women is u = 63.8 inches, with a standard deviation of o = 2.8 inches. Who is taller relative to their gender, a man 73 inches tall, or a woman 68 inches tall? Work through this problem in steps: The man's height is X = The men's mean is = The men's standard deviation is The man's z-score is z = (x - p)/o = ( _- So standard deviations from the mean Zman = The woman's height is x = The women's mean is The women's standard deviation is The woman's z-score is z = (x - p)/o = (___- standard deviations from the mean So Zwoman %3D Which one is larger? Example 2: 0.00, 0.08, 0.13, 0.14, 0.16, 0.17, 0.20, 0.29, .056, 0.70, 0.79 L = .25(11) = 2.75 which rounds to 3, so the 3rd number is the 25th percentile and its value is L = .50(11) = 5.5 which rounds to 6, so the 6th number is the 50th percentile, or the median and its value is L = .75(11) = 8.25 which rounds to 9, so the 9th number is the 75th
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Transcribed Image Text:Math 11 Elementary Statistics
In Class 3.3
Measures of Position (or location)
Name
Date
Example 1: Computing and interpreting z-
Scores
A National Center for Health Statistics study states that the mean height for
adult men in the United States is u = 69.4 inches, with a standard deviation
of o = 3.1 inches. The mean height for adult women is u = 63.8 inches, with
a standard deviation of o = 2.8 inches. Who is taller relative to their gender,
a man 73 inches tall, or a woman 68 inches tall?
Work through this problem in steps:
The man's height is
X =
The men's mean is
The men's standard deviation is
O =
The man's z-score is
z = (x - p)/o = (__-
So
Zman
standard deviations from the mean
The woman's height is
X =
The women's mean is
The women's standard deviation is
O =
The woman's z-score is
z = (x - p)/o = (_
standard deviations from the mean
So
%3D
Zwoman
Which one is larger?
Example 2:
0.00, 0.08, 0.13, 0.14, 0.16, 0.17, 0.20, 0.29, .056, 0.70, 0.79
L = .25(11) = 2.75 which rounds to 3, so the 3rd number is the 25th
percentile
and its value is
L = .50(11) = 5.5 which rounds to 6, so the 6th number is the 50th
percentile, or the median
and its value is
L = .75(11) = 8.25 which rounds to 9, so the 9th number is the 75h
![percentile
and its value is
Example 3: Use the same data, from example 2.
L = .60(11) = 6.6 which rounds to 7, so the 7th number is the 60th
percentile
and its value is
Example 4: Use the same data, from example 2.
Find the percentile of 0.29
There are 7 values less than 0.29
The percentile = 100[(7 + 0.5)/11] = 68.18 or 68.2
So the result 0.29 corresponds to the 68" percentile.
Example 5: complete the table.
Use the same data, from example 2.
Min. Q, Q2 or Med Q, Max
Please use a copy of the text read to and complete the in-class assignment.
You may work on this page or use your own lined paper or graph paper in
you prefer.
In class assignment, problems: 11, 13, 17, 21 and 25
In Exercises 9-12, fill in each blank with the appropriate
word or phrase.
11The quantity Q - Q, is known as the
In Exercises 13-16, determine whether the statement is
true or false. If the statement is false, rewrite it as a true
statement.
13The third quartile, Q3, separates the lowest 25% of the data from the
12 of 14](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87e7ed97-c167-45cc-b510-5bd999d5e24d%2F361dca08-8432-452b-b92e-b40641ef2392%2Fljo60hw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:percentile
and its value is
Example 3: Use the same data, from example 2.
L = .60(11) = 6.6 which rounds to 7, so the 7th number is the 60th
percentile
and its value is
Example 4: Use the same data, from example 2.
Find the percentile of 0.29
There are 7 values less than 0.29
The percentile = 100[(7 + 0.5)/11] = 68.18 or 68.2
So the result 0.29 corresponds to the 68" percentile.
Example 5: complete the table.
Use the same data, from example 2.
Min. Q, Q2 or Med Q, Max
Please use a copy of the text read to and complete the in-class assignment.
You may work on this page or use your own lined paper or graph paper in
you prefer.
In class assignment, problems: 11, 13, 17, 21 and 25
In Exercises 9-12, fill in each blank with the appropriate
word or phrase.
11The quantity Q - Q, is known as the
In Exercises 13-16, determine whether the statement is
true or false. If the statement is false, rewrite it as a true
statement.
13The third quartile, Q3, separates the lowest 25% of the data from the
12 of 14
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