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Averages and dispersion
On today’s menu ,[object Object],[object Object],[object Object],[object Object]
Measures of central tendency ,[object Object],[object Object],[object Object],[object Object]
Where is mean? Where is median? There is a way of showing a difference…
Dispersion ,[object Object],[object Object],[object Object]
Fairly spread out distribution – Higher IQR More spread out data More compact distribution Lower IQR, less spread out data, more consistent
Wide dispersion, more variation, less consistent Narrow dispersion, less variation, more consistent Same mean mode median Different dispersions
Mean from distribution Total gives number of people Total of this column gives an  estimate  of total height… 12 155-159 8 150-154 441 3 147 145-149 X × F F X Group
Mean formula “ Sum of the x times the f” “ Sum of fs” The mean symbol
Cumulative frequency table Each figure in this column is the sum of the frequencies up to that line Must use the UCB here – NOT the midpoint 12 155-159 11 8 154.5 150-154 3 3 149.5 145-149 CF F UCB Group
CF Questions… ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Plotting the curve ,[object Object],[object Object],[object Object],[object Object]
Median…. Upper Quartile (UQ)‏ Lower Quartile (LQ)‏
IQR ,[object Object],[object Object],[object Object]
Box and whisker plot Median Drawn on same set of axes – really good Comparison of two frequency tables… Max Min LQ UQ

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Averages And Spread

  • 2.
  • 3.
  • 4. Where is mean? Where is median? There is a way of showing a difference…
  • 5.
  • 6. Fairly spread out distribution – Higher IQR More spread out data More compact distribution Lower IQR, less spread out data, more consistent
  • 7. Wide dispersion, more variation, less consistent Narrow dispersion, less variation, more consistent Same mean mode median Different dispersions
  • 8. Mean from distribution Total gives number of people Total of this column gives an estimate of total height… 12 155-159 8 150-154 441 3 147 145-149 X × F F X Group
  • 9. Mean formula “ Sum of the x times the f” “ Sum of fs” The mean symbol
  • 10. Cumulative frequency table Each figure in this column is the sum of the frequencies up to that line Must use the UCB here – NOT the midpoint 12 155-159 11 8 154.5 150-154 3 3 149.5 145-149 CF F UCB Group
  • 11.
  • 12.
  • 13. Median…. Upper Quartile (UQ)‏ Lower Quartile (LQ)‏
  • 14.
  • 15. Box and whisker plot Median Drawn on same set of axes – really good Comparison of two frequency tables… Max Min LQ UQ