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Statistics

Histograms
  • A histogram displays the frequency of either continuous or grouped discrete data in the form of bars.
  • The bars are joined together.
  • The bars can be of varying width.
  • The frequency of the data is represented by the area of the bar and not the height.
  • When class intervals are different, it is the area of the bar which represents the frequency, not the height.
  • Instead of frequency being plotted on the vertical axis, frequency density is plotted.
  • Class width = Interval
  • Frequency density = Height
  • Frequency = Class width × Frequency density
Averages
  • Mean:
  • Median:
    • is the middle value when the data has been written in ascending or descending order.
    • For an even number of values: add the two numbers in the middle and divide by 2.
  • Mode: is the most frequently occurring value
  • Range: is the difference between the highest and lowest values.
  • Estimated mean of grouped data:
    • Work out the midpoints of each group and multiply by the frequency.
    • Then divide by the number of values.
Cumulative Frequency
  • Cumulative frequency is the total frequency up to a given point.
  • Inter-quartile range = upper quartile – lower quartile.

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