Interpreting-Cumulative-Frequency-Diagrams Aqa Higher

Interpreting cumulative frequency diagrams

How do I use and interpret a cumulative frequency diagram?

• A cumulative frequency diagram provides a way to estimate key facts about the data

  • median 

  • lower and upper quartiles (and interquartile range)

  • percentiles

• These values will be estimates as the original raw data is unknown

  • Cumulative frequency diagrams are used with grouped data 

  • Points are joined by a smooth curve

    • This means the data is assumed to be smoothly spread out over each interval

How do I find the median, lower quartile and upper quartile from a cumulative frequency diagram?

• This is all about understanding how many data values are represented by the cumulative frequency diagram

  • This may be stated in words within the question

  • If not, it will be the highest value on the frequency (y-) axis that the curve on the diagram reaches

    • This should be “top right” of the curve on a cumulative frequency diagram

• Finding the median:

  • STEP 1
    Find the position of the median, for data values, this will be 

    • This is different from finding the median from a set of data values

    • E.g. for a list of 60 data values the median would be halfway between the 30th and 31st values

    • But for a cumulative frequency diagram it would just be

  • STEP 2
    Draw a horizontal line from  on the cumulative frequency (y-) axis until it hits the curve

  • STEP 3
    Draw a vertical line from that point on the curve down to the horizontal (x-) axis

    • The value where that line hits the horizontal axis will be the median

• Finding the lower quartile:

  • STEP 1
    Find the position of the lower quartile

    • For data values this will be 

  • STEP 2
    Draw a horizontal line from  on the cumulative frequency axis until it hits the curve

  • STEP 3
    Draw a vertical line from that point on the curve down to the horizontal (x-) axis

    • The value where that line hits the horizontal axis will be the lower quartile

• Finding the upper quartile:

  • STEP 1
    Find the position of the upper quartile

    • For data values this will be <img alt=”fraction numerator 3 n over denominator 4 end fraction space open parentheses straight i. straight e. space space 3 cross times n over 4 close parentheses” data-mathml='<math ><semantics><mrow><mfrac><mrow><mn>3</mn><mi>n</mi></mrow><mn>4</mn></mfrac><mo> </mo><mfenced><mrow><mi mathvariant=”normal”>i</mi><mo>.</mo><mi mathvariant=”normal”>e</mi><mo>.</mo><mo> </mo><mo> </mo><mn>3</mn><mo>×</mo><mfrac><mi>n</mi><mn>4</mn></mfrac></mrow></mfenced></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ role=”math” 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