Linear-Interpolation gcse Edexcel

Median from Grouped Data

How do I find the median for grouped data?

• Grouped data doesn’t contain the individual data values

  • So we can’t find the exact median in the usual way

• We can estimate the median for grouped data using linear interpolation

  • This assumes the data is evenly spread across the class containing the median

• STEP 1
  Identify the class interval containing the median

  • This is the class containing the ‘^th’ data value

    • Divide the total number of values, n, by 2

  • e.g. if there are 80 data values,

    • Consider cumulative frequencies until you find the class interval containing the 40^th value

• STEP 2
  Find ‘how far into’ that class interval the ^th data value is

  • e.g. if the interval with the median contains the 36^th through 43^rd data values

    • then the 40^th value is ‘5 values in’ (36, 37, 38, 39, 40)

    • and there are 8 values in the interval

    • so the 40^th value isof the way into the interval

• STEP 3
  Multiply the class width of the class interval containing the median by the fraction found in Step 2

  • e.g. if the interval with the median is

    • the class width is

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