Representation of Data

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  • Representation of Data
    • Stem and Leaf
      • Advantages
        • They still have all details of the data
        • They allow direct comparisons of two sets of data
        • They give a sense of location and spread
      • Key Points
        • Always put values in order from the centre
        • Make sure values in leaf are always one digit
        • Spilt data up to ensure you show a shape
        • Always include titles and a key
      • How To Read From Stem And Leaf
        • Mode = Most Comman
        • Range= biggest - smallest
        • Median = number of values / 2
          • Interquartile Range = Q3-Q1
        • Lower Quartile = Number of values /4
    • Box Plots
      • Advantages
        • Shows location and spread at a glance
        • Always use clear labels for each box plot and scale
      • Outliers
        • Are generally found using 1.5 x IQR
          • Then subtract from LQ if anything is below this then it is an outlier
          • Add to UQ if anything is above this it is an outlier
    • Histograms
      • Key Points
        • Histograms are used for continious data
        • If a table does not show continuous data you must alter the class boundaries
        • Frequencey Density = (frequency /class width)
        • The area of the bar is proportional to the frequency
        • The modal group is the group with the largest area
        • to calculate the height of each bar use the formula  k x frequency
    • Skewness
      • box plots positive: Q2-Q1 < Q3 -Q2
        • Negative: Q2-Q1 > Q3 -Q2
          • Symmetrical: Q2-Q1 = Q3 -Q2
      • histograms 3(mean-median)/ standard deviation
        • Positive: mode< median< mean
          • Negative:  mode> median> mean


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