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# 2 6 measure of position

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### Transcript

• 1. Measure of Position
• Looking at individual values: Where does it lie among the sample (or population)
• standard score (or z score)
• quartiles, deciles, and percentiles
• 25%-75% SAT scores
• Princeton 1370 – 1560
• Villanova 1180 – 1340
• 2. Standard Score (z score)
• How many standard deviations from the mean is a sample?
• Z scores less that –2.00 or greater that 2.00 are outliers.
• 3. For example
• 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
• Mean : 77
• Standard deviation = 18
mean mean +  mean + 2  mean + 3  mean - 3  mean - 2  mean - 1 
• 4. Quartiles
• Separates the sorted list into four parts separated by three boundaries
min lower quartile median max upper quartile 25% 25% 25% 25%
• If the median separates the list into two halves
• The lower quartile is the median of the lower half
• The upper quartile is the median of the upper half
• 5. For example
• 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
• 6. Deciles
• 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
min median max 10% 10% 10%
• 7. Percentile
• Percentile value of a value x
• Where does x sit in a set of data
• For example:
• 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
• What is the percentile of:
• 8. Finding the value at the k th Percentile
• n values in our sample
• Data has to be sorted
• Compute L, the position of the k th percentile
• If L is a whole number, the percentile is midway between L and L+1
• If L is a decimal, round up; the percentile is the L th value
• 9. For example
• 25 55 59 59 63 71 71 74 80 80 80 83 84 84 87 88 95 95 100 100
• What is the value at the
• 10. Relationships
• The 1 st quartile is the same as the 25 th percentile
• The 3 rd quartile is the same as the 75 th percentile
• The first decile is the same as the 10 th percentile
• 11. Live example
• What are the mean and standard deviation
• What are the minimum, lower quartile, median, upper quartile, and maximum
• What is the 4 th decile
• What is the 35% percentile?
• What is South’s z value
• What is South’s percentile?