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Find the following for the Weight of Football Players
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Fun Coming Up!
Homework for Chapter 3Due Tuesday Oct 2nd.Test on Chapter 3Thursday Oct 4, 2012.
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Bluman, Chapter 3
3-3 Measures of Position Z-score
Percentile
Quartile Outlier
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Bluman, Chapter 3
Measures of Position: Z-score
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Bluman, Chapter 3
Measures of Position: Z-score A z-score or standard score for a value is
obtained by following formulas:
A z-score represents the number of standard deviations a value is above or below the mean.
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Rounding Rule for Z score
Round the Z score to 2 decimal places.
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Chapter 3Data Description
Section 3-3Example 3-29Page #142
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Example 3-29: Test ScoresA student scored 65 on a calculus test that had a mean of 50 and a standard deviation of 10; she scored 30 on a history test with a mean of 25 and a standard deviation of 5. Compare her relative positions on the two tests.
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Example 3-29: Test ScoresA student scored 65 on a calculus test that had a mean of 50 and a standard deviation of 10; she scored 30 on a history test with a mean of 25 and a standard deviation of 5. Compare her relative positions on the two tests.
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Example 3-29: Test ScoresA student scored 65 on a calculus test that had a mean of 50 and a standard deviation of 10; she scored 30 on a history test with a mean of 25 and a standard deviation of 5. Compare her relative positions on the two tests.
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Example 3-29: Test ScoresA student scored 65 on a calculus test that had a mean of 50 and a standard deviation of 10; she scored 30 on a history test with a mean of 25 and a standard deviation of 5. Compare her relative positions on the two tests.
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She has a higher relative position in the Calculus class.
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Percentiles
Percentiles divides the data into 100 equal groups.
Percentiles are symbolized by P1, P2, P3, …,P99
Please take a look at data on page 135 of your text.
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Formula
Percentile formula:
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Check this website out!
There are variation on the formula for Percentiles. The website below does a fantastic job of displaying and explaining the variations.
http://www.regentsprep.org/regents/math/algebra/AD6/quartiles.htm
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Definition 1: A percentile is a measure that tells us what percent of the total frequency scored at or below that measure. A percentile rank is the percentage of scores that fall at or below a given score.
Definition 2: A percentile is a measure that tells us what percent of the total frequency scored below that measure. A percentile rank is the percentage of scores that fall below a given score.
Formula:To find the percentile rank of a score, x, out of a set of n scores, where x is included: Where B = number of scores below x E = number of scores equal to x n = number of scores
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About Percentile Ranks:
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About Percentile Ranks:
Percentile rank is a number between 0 and 100 indicating the percent of cases falling at or below that score.
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About Percentile Ranks:
Percentile rank is a number between 0 and 100 indicating the percent of cases falling at or below that score.
Scores are divided into 100 equally sized groups.
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About Percentile Ranks:
Percentile rank is a number between 0 and 100 indicating the percent of cases falling at or below that score.
Scores are divided into 100 equally sized groups.
Percentile ranks are usually written to the nearest whole percent: 74.5% = 75% = 75th percentile.
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About Percentile Ranks:
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About Percentile Ranks:
Scores are arranged in rank order from lowest to highest
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About Percentile Ranks:
Scores are arranged in rank order from lowest to highest
There is no 0 percentile rank-the lowest score is the 1st percentile.
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About Percentile Ranks:
Scores are arranged in rank order from lowest to highest
There is no 0 percentile rank-the lowest score is the 1st percentile.
There is no 100th percentile- the highest score is the 99th percentile.
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About Percentile Ranks:
Scores are arranged in rank order from lowest to highest
There is no 0 percentile rank-the lowest score is the 1st percentile.
There is no 100th percentile- the highest score is the 99th percentile.
You can’t perform the same mathematical operations on percentile that you can on raw scores. You can’t, for example, compute the mean of percentile scores.
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Bluman, Chapter 3
Example 3-31
The frequency distribution for the systolic blood pressure readings (mm of mercury) of 200 randomly selected college students is shown here. Construct a percentile graph
Page 146
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A B C D
Class Boundaries
Frequency Cumulative Freq
Cumulative Percent
89.5-104.5 24
104.5-119.5 62
119.5-134.5 72
134.5-149.5 26
149.5-164.5 12
164.5-179.5 4 200 200 200 200
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Bluman, Chapter 3
Measures of Position: Example of a Percentile Graph
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Chapter 3Data Description
Section 3-3Example 3-32Page #147
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Example 3-32
A teacher gives a 20-point test to 10 students. The scores are shown here.
18,15,12,6,8,2,3,5,20,10 Find the percentile rank of a score of 12?
6?
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Example 3-32: Test Scores
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Example 3-32: Test ScoresA teacher gives a 20-point test to 10 students. Find the percentile rank of a score of 12.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
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Example 3-32: Test ScoresA teacher gives a 20-point test to 10 students. Find the percentile rank of a score of 12.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
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Example 3-32: Test ScoresA teacher gives a 20-point test to 10 students. Find the percentile rank of a score of 12.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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19Friday, January 25, 13
Example 3-32: Test ScoresA teacher gives a 20-point test to 10 students. Find the percentile rank of a score of 12.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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19Friday, January 25, 13
Example 3-32: Test ScoresA teacher gives a 20-point test to 10 students. Find the percentile rank of a score of 12.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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19Friday, January 25, 13
Example 3-32: Test ScoresA teacher gives a 20-point test to 10 students. Find the percentile rank of a score of 12.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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19Friday, January 25, 13
Example 3-32: Test ScoresA teacher gives a 20-point test to 10 students. Find the percentile rank of a score of 12.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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6 values
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Example 3-32: Test ScoresA teacher gives a 20-point test to 10 students. Find the percentile rank of a score of 12.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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6 values
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Example 3-32: Test ScoresA teacher gives a 20-point test to 10 students. Find the percentile rank of a score of 12.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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6 values
A student whose score was 12 did better than 65% of the class.
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Refer to the same data
Find the value of the 25th percentile? 60th?
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Refer to the same data
Find the value of the 25th percentile? 60th?
If the percentile is known, then the formula is
See page 149 for full explanation
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Example 3-34: Test Scores
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Example 3-34: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 25th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
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Example 3-34: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 25th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
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Example 3-34: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 25th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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Example 3-34: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 25th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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Example 3-34: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 25th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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Example 3-34: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 25th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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Example 3-34: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 25th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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This is the location of data. i.e. 3rd value.
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Example 3-34: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 25th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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This is the location of data. i.e. 3rd value.
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Example 3-34: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 25th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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The value 5 corresponds to the 25th percentile.
This is the location of data. i.e. 3rd value.
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Example 3-35: Test Scores
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Example 3-35: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 60th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
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Example 3-35: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 60th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
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Example 3-35: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 60th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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22Friday, January 25, 13
Example 3-35: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 60th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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22Friday, January 25, 13
Example 3-35: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 60th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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Example 3-35: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 60th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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The answer is between the 6th and 7th data point.
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Example 3-35: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 60th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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The answer is between the 6th and 7th data point.
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Example 3-35: Test ScoresA teacher gives a 20-point test to 10 students. Find the value corresponding to the 60th percentile.
18, 15, 12, 6, 8, 2, 3, 5, 20, 10
Sort in ascending order.2, 3, 5, 6, 8, 10, 12, 15, 18, 20
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The value 11 corresponds to the 60th percentile.
The answer is between the 6th and 7th data point.
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Bluman, Chapter 3
Measures of Position: Deciles Deciles separate the data set into 10
equal groups. D1=P10, D4=P40
Please Pages 150-151 for further instructions.
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Bluman, Chapter 3
Measures of Position: Quartiles
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Bluman, Chapter 3
Measures of Position: Quartiles
Quartiles separate the data set into 4 equal groups. Q1=P25, Q2=MD, Q3=P75
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Bluman, Chapter 3
Measures of Position: Quartiles
Quartiles separate the data set into 4 equal groups. Q1=P25, Q2=MD, Q3=P75
Q2 = median(Low,High)
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Bluman, Chapter 3
Measures of Position: Quartiles
Quartiles separate the data set into 4 equal groups. Q1=P25, Q2=MD, Q3=P75
Q2 = median(Low,High)Q1 = median(Low,Q2)
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24Friday, January 25, 13
Bluman, Chapter 3
Measures of Position: Quartiles
Quartiles separate the data set into 4 equal groups. Q1=P25, Q2=MD, Q3=P75
Q2 = median(Low,High)Q1 = median(Low,Q2) Q3 = median(Q2,High)
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Bluman, Chapter 3
Measures of Position: Quartiles
Quartiles separate the data set into 4 equal groups. Q1=P25, Q2=MD, Q3=P75
Q2 = median(Low,High)Q1 = median(Low,Q2) Q3 = median(Q2,High)
The Interquartile Range, IQR = Q3 – Q1.
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Chapter 3Data Description
Section 3-3Example 3-36Page #150
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Example 3-36: Quartiles
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Example 3-36: QuartilesFind Q1, Q2, and Q3 for the data set.
15, 13, 6, 5, 12, 50, 22, 18
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Example 3-36: QuartilesFind Q1, Q2, and Q3 for the data set.
15, 13, 6, 5, 12, 50, 22, 18
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26Friday, January 25, 13
Example 3-36: QuartilesFind Q1, Q2, and Q3 for the data set.
15, 13, 6, 5, 12, 50, 22, 18
Sort in ascending order.5, 6, 12, 13, 15, 18, 22, 50
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Example 3-36: QuartilesFind Q1, Q2, and Q3 for the data set.
15, 13, 6, 5, 12, 50, 22, 18
Sort in ascending order.5, 6, 12, 13, 15, 18, 22, 50
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26Friday, January 25, 13
Example 3-36: QuartilesFind Q1, Q2, and Q3 for the data set.
15, 13, 6, 5, 12, 50, 22, 18
Sort in ascending order.5, 6, 12, 13, 15, 18, 22, 50
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26Friday, January 25, 13
Example 3-36: QuartilesFind Q1, Q2, and Q3 for the data set.
15, 13, 6, 5, 12, 50, 22, 18
Sort in ascending order.5, 6, 12, 13, 15, 18, 22, 50
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26Friday, January 25, 13
Example 3-36: QuartilesFind Q1, Q2, and Q3 for the data set.
15, 13, 6, 5, 12, 50, 22, 18
Sort in ascending order.5, 6, 12, 13, 15, 18, 22, 50
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26Friday, January 25, 13
Example 3-36: QuartilesFind Q1, Q2, and Q3 for the data set.
15, 13, 6, 5, 12, 50, 22, 18
Sort in ascending order.5, 6, 12, 13, 15, 18, 22, 50
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26Friday, January 25, 13
Example 3-36: QuartilesFind Q1, Q2, and Q3 for the data set.
15, 13, 6, 5, 12, 50, 22, 18
Sort in ascending order.5, 6, 12, 13, 15, 18, 22, 50
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Bluman, Chapter 3
Measures of Position: Outliers
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Please refer to page 152 of your test for the procedure of how to identify the outliers.
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Bluman, Chapter 3
Measures of Position: Outliers An outlier is an extremely high or low data
value when compared with the rest of the data values.
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Please refer to page 152 of your test for the procedure of how to identify the outliers.
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Bluman, Chapter 3
Measures of Position: Outliers An outlier is an extremely high or low data
value when compared with the rest of the data values.
A data value less than Q1 – 1.5(IQR) or greater than Q1 + 1.5(IQR) can be considered an outlier.
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Please refer to page 152 of your test for the procedure of how to identify the outliers.
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Homework
Read section 3-3 and study the relevant examples.
Page 153 #1-8 all, 11-31 odds
Highly recommended:TI83- TI84 Step by Step
Pages 158-159
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