Averages and dispersion

On today’s menu Bread basket: stats vocabulary Starter: Mean from frequency table Main: Cumulative frequency diagram, median, IQR Sweet: Median and mode from frequency table

Bread basket: stats vocabulary

Starter: Mean from frequency table

Main: Cumulative frequency diagram, median, IQR

Sweet: Median and mode from frequency table

Measures of central tendency Not a political policy! Averages like mean , median , mode Tells you a typical value for a set of data But you need to know how typical the average is…

Not a political policy!

Averages like mean , median , mode

Tells you a typical value for a set of data

But you need to know how typical the average is…

Where is mean? Where is median? There is a way of showing a difference…

Dispersion Dispersion says how spread out the data is Measures of dispersion includes the ‘range’ and…. The Inter Quartile Range (coming soon)‏

Dispersion says how spread out the data is

Measures of dispersion includes the ‘range’ and….

The Inter Quartile Range (coming soon)‏

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… How many below than 179.5 cm Look up 179.5 in UCB column Corresponding CF is the answer How many above than 169.5 cm Look up 169.5 cm in UCB column 96 – CF gives number taller than 169.5 Median: find which group 48 th person is in….

How many below than 179.5 cm

Look up 179.5 in UCB column

Corresponding CF is the answer

How many above than 169.5 cm

Look up 169.5 cm in UCB column

96 – CF gives number taller than 169.5

Median: find which group 48 th person is in….

Plotting the curve Plot the UCBs on the horizontal Plot the Cumulative Frequencies on the vertical axis Plot an ‘ imaginary point’ at CF zero before the first point Draw smooth curve thru’ the points

Plot the UCBs on the horizontal

Plot the Cumulative Frequencies on the vertical axis

Plot an ‘ imaginary point’ at CF zero before the first point

Draw smooth curve thru’ the points

Median…. Upper Quartile (UQ)‏ Lower Quartile (LQ)‏

IQR Inter-quartile range is simply IQR = UQ – LQ The IQR tells you the range of the ‘middle 50%’ If the median wage was (say) £160 and the IQR was £200 then the middle 50% earned from £60 to £260…

Inter-quartile range is simply IQR = UQ – LQ

The IQR tells you the range of the ‘middle 50%’

If the median wage was (say) £160 and the IQR was £200 then the middle 50% earned from £60 to £260…

Box and whisker plot Median Drawn on same set of axes – really good Comparison of two frequency tables… Max Min LQ UQ