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

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…

Where is mean?Where is median?

There is a way ofshowing a difference…

Dispersion

• Dispersion says how spread out the data is

• Measures of dispersion includes the ‘range’ and….

• The Inter Quartile Range (coming soon)

Same meanmode median

Wide dispersion, more variation, less consistent

Differentdispersions Narrow

dispersion, less variation, more consistent

Mean from distribution

12155-159

8150-154

4413147145-149

X × FFXGroup

Total gives number of people

Total of this column gives an estimate of total height…

Mean formula

f

xfx

“Sum of the x times the f”

“Sum of fs”

The mean symbol

Cumulative frequency table

12155-159

118154.5150-154

33149.5145-149

CFFUCBGroup

Each figure in this column is the sum of the frequencies up to that line

Must use the UCB here – NOT the midpoint

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 48th

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

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…

Box and whisker plot

MaxMin LQ

UQMedian

Drawn on same set of axes – really goodComparison of two frequency tables…