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# 2 6 measure of position

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### 2 6 measure of position

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