Averages and dispersion
On today’s menu <ul><li>Bread basket:  stats vocabulary </li></ul><ul><li>Starter:  Mean from frequency table </li></ul><u...
Measures of central tendency <ul><li>Not a political policy! </li></ul><ul><li>Averages like  mean ,  median ,  mode </li>...
Where is mean? Where is median? There is a way of showing a difference…
Dispersion <ul><li>Dispersion says  how spread out  the data is </li></ul><ul><li>Measures of dispersion includes the ‘ran...
Fairly spread out distribution – Higher IQR More spread out data More compact distribution Lower IQR, less spread out data...
Wide dispersion, more variation, less consistent Narrow dispersion, less variation, more consistent Same mean mode median ...
Mean from distribution Total gives number of people Total of this column gives an  estimate  of total height… 12 155-159 8...
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 ...
CF Questions… <ul><li>How many  below  than 179.5 cm </li></ul><ul><ul><li>Look up 179.5 in UCB column </li></ul></ul><ul>...
Plotting the curve <ul><li>Plot the  UCBs on the horizontal </li></ul><ul><li>Plot the  Cumulative Frequencies on the vert...
Median…. Upper Quartile (UQ)‏ Lower Quartile (LQ)‏
IQR <ul><li>Inter-quartile range is simply  IQR = UQ – LQ </li></ul><ul><li>The IQR tells you the range of the ‘middle 50%...
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

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This powerpoint with a number of examples of each topic lasted for a 1.5 hour lesson.Plenty of practical graph drawing. Some of the custom builds don't work on slideshare

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Averages And Spread

  1. 1. Averages and dispersion
  2. 2. On today’s menu <ul><li>Bread basket: stats vocabulary </li></ul><ul><li>Starter: Mean from frequency table </li></ul><ul><li>Main: Cumulative frequency diagram, median, IQR </li></ul><ul><li>Sweet: Median and mode from frequency table </li></ul>
  3. 3. Measures of central tendency <ul><li>Not a political policy! </li></ul><ul><li>Averages like mean , median , mode </li></ul><ul><li>Tells you a typical value for a set of data </li></ul><ul><li>But you need to know how typical the average is… </li></ul>
  4. 4. Where is mean? Where is median? There is a way of showing a difference…
  5. 5. Dispersion <ul><li>Dispersion says how spread out the data is </li></ul><ul><li>Measures of dispersion includes the ‘range’ and…. </li></ul><ul><li>The Inter Quartile Range (coming soon)‏ </li></ul>
  6. 6. Fairly spread out distribution – Higher IQR More spread out data More compact distribution Lower IQR, less spread out data, more consistent
  7. 7. Wide dispersion, more variation, less consistent Narrow dispersion, less variation, more consistent Same mean mode median Different dispersions
  8. 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. 9. Mean formula “ Sum of the x times the f” “ Sum of fs” The mean symbol
  10. 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. 11. CF Questions… <ul><li>How many below than 179.5 cm </li></ul><ul><ul><li>Look up 179.5 in UCB column </li></ul></ul><ul><ul><li>Corresponding CF is the answer </li></ul></ul><ul><li>How many above than 169.5 cm </li></ul><ul><ul><li>Look up 169.5 cm in UCB column </li></ul></ul><ul><ul><li>96 – CF gives number taller than 169.5 </li></ul></ul><ul><li>Median: find which group 48 th person is in…. </li></ul>
  12. 12. Plotting the curve <ul><li>Plot the UCBs on the horizontal </li></ul><ul><li>Plot the Cumulative Frequencies on the vertical axis </li></ul><ul><li>Plot an ‘ imaginary point’ at CF zero before the first point </li></ul><ul><li>Draw smooth curve thru’ the points </li></ul>
  13. 13. Median…. Upper Quartile (UQ)‏ Lower Quartile (LQ)‏
  14. 14. IQR <ul><li>Inter-quartile range is simply IQR = UQ – LQ </li></ul><ul><li>The IQR tells you the range of the ‘middle 50%’ </li></ul><ul><li>If the median wage was (say) £160 and the IQR was £200 then the middle 50% earned from £60 to £260… </li></ul>
  15. 15. 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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