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# Center 5#Summary

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### Center 5#Summary

1. 1. Numerically
2. 2. <ul><li>Mean: arithmetic average, add all observations together and divide by the number of observations. </li></ul><ul><li>If there are n observations which are labeled as ; </li></ul><ul><li>The mean is </li></ul><ul><li>Read as “x bar” </li></ul><ul><li>Must be written with the bar!!!! </li></ul>
3. 4. <ul><li>the middle obsevation </li></ul><ul><li>Arrange the data in order from least to greatest </li></ul><ul><li>If an odd number of obs. find the middle number </li></ul><ul><li>If an even number of obs. find the average of the middle two numbers </li></ul>
4. 5. <ul><li>Order: </li></ul><ul><li>2 2 3 4 5 5 6 6 7 7 7 7 7 8 9 9 9 10 11 12 14 16 19 27 35 </li></ul><ul><li>Med = </li></ul>
5. 6. <ul><li>If the distribution is symmetric the mean the median will be approximately the same </li></ul><ul><li>If the distribution is skewed to the left, the mean will be less than the median </li></ul><ul><li>If the distribution is skewed to the right, the mean will be higher than the median </li></ul><ul><li>The mean is affected by outliers and the median is resistant to outliers </li></ul><ul><li>When the data is symmetric use the mean </li></ul><ul><li>When the data is skewed use the median </li></ul>
6. 7. <ul><li>Numeric description of the distribution </li></ul><ul><li>Minimum </li></ul><ul><li>1 st Quartile (Q 1 ) – Middle number of the bottom half of the data </li></ul><ul><li>Median </li></ul><ul><li>3 rd Quartile (Q 3 ) – Middle number of the top half of the data </li></ul><ul><li>Maximum </li></ul>
7. 8. <ul><li>Put data in order </li></ul><ul><li>2 2 3 4 5 5 6 6 7 7 7 7 7 8 9 9 9 10 11 12 14 16 19 27 35 </li></ul><ul><li> </li></ul>Min = 2 Q 1 = 5.5 Med = 7 Q 3 = 11.5 Max = 35
8. 9. <ul><li>Graphical display of 5 number summary </li></ul>
9. 10. <ul><li>Range = Max – Min </li></ul><ul><li>  </li></ul><ul><li>Interquartile Range </li></ul><ul><li>IQR = Q 3 – Q 1 </li></ul>
10. 11. <ul><li>Any observation below the Lower Fence (LF) or above the Upper Fence (UF) is considered an outlier </li></ul><ul><li>LF = Q 1 – 1.5(IQR) </li></ul><ul><li>UF = Q 3 + 1.5(IQR) </li></ul>
11. 12. <ul><li>If outliers are present the whisker extends to the last value not an outlier </li></ul><ul><li>The outlier is marked with an x, box, or point </li></ul>