# Measures of Position

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Measures of Position. Percentiles Z-scores. The following represents my results when playing an online sudoku gameat www.websudoku.com. 30 min. 0 min. Introduction. A student gets a test back with a score of 78 on it. A 10 th -grader scores 46 on the PSAT Writing test - PowerPoint PPT Presentation

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• Measures of PositionPercentilesZ-scores

• 0 min30 minThe following represents my results when playing an online sudoku gameat www.websudoku.com.

• IntroductionA student gets a test back with a score of 78 on it.A 10th-grader scores 46 on the PSAT Writing test

Isolated numbers dont always provide enough informationwhat we want to know is where we stand.

• Where Do I Stand?Lets make a dotplot of our heights from 58 to 78 inches.How many people in the class have heights less than you?What percent of the dents in the class have heights less than yours?This is your percentile in the distribution of heights

• Finishing.Calculate the mean and standard deviation.

Where does your height fall in relation to the mean: above or below?

How many standard deviations above or below the mean is it?This is the z-score for your height.

• Lets discussWhat would happen to the classs height distribution if you converted each data value from inches to centimeters. (2.54cm = 1 in)

How would this change of units affect the measures of center, spread, and location (percentile & z-score) that you calculated.

• National Center for Health StatisticsLook at Clinical Growth Charts at www.cdc.gov/nchs

• PercentilesValue such that r% of the observations in the data set fall at or below that value.

If you are at the 75th percentile, then 75% of the students had heights less than yours.

• Test scores on last AP Test. Jenny made an 86. How did she perform relative to her classmates?Her score was greater than 21 of the 25 observations. Since 21 of the 25, or 84%, of the scores are below hers, Jenny is at the 84th percentile in the classs test score distribution. 6 77 23347 57778998 001233348 5699 03

• Find the percentiles for the following students.Mary, who earned a 74.

Two students who earned scores of 80.6 77 23347 57778998 001233348 5699 03

• Cumulative Relative Frequency Table:

• Cumulative Relative Frequency Graph:

Chart1

0

4.5

20.5

50

77.3

93.2

100

Y-Value 1

Age at inauguration

Cumulative relative frequency (%)

Sheet1

X-ValuesY-Value 1

400

454.5

5020.5

5550

6077.3

6593.2

70100

• InterpretingWhy does it get very steep beginning at age 50?

When does it slow down? Why?

What percent were inaugurated before age 70?

Whats the IQR?

Obama was 47.

Chart1

0

4.5

20.5

50

77.3

93.2

100

Y-Value 1

Age at inauguration

Cumulative relative frequency (%)

Sheet1

X-ValuesY-Value 1

400

454.5

5020.5

5550

6077.3

6593.2

70100

• Describing Location in a DistributionUse the graph from page 88 to answer the following questions.Was Barack Obama, who was inaugurated at age 47, unusually young?Estimate and interpret the 65th percentile of the distribution

Interpreting Cumulative Relative Frequency Graphs

47116558

Chart1

0

4.5

20.5

50

77.3

93.2

100

Y-Value 1

Age at inauguration

Cumulative relative frequency (%)

Sheet1

X-ValuesY-Value 1

400

454.5

5020.5

5550

6077.3

6593.2

70100

• Median Income for US and District of Columbia.

• Graph it:

• What is the relationship between percentiles and quartiles?

• Z-Score (standardized score)It represents the number of deviations from the mean.If its positive, then its above the mean.If its negative, then its below the mean.It standardized measurements since its in terms of st. deviation.

• Discovery:Mean = 90St. dev = 10Find z score for 809573

• Z-Score Formula

• Compareusing z-score.History TestMean = 92St. Dev = 3My Score = 95Math TestMean = 80St. Dev = 5My Score = 90

• CompareMath: mean = 70 x = 62 s = 6

English: mean = 80 x = 72 s = 3

• Be Careful!Being better is relative to the situation.

What if I wanted to compare race times?

• HomeworkPage 105 (1-15) odd

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