Range & Interquartile Range (SQA National 5 Applications of Mathematics): Revision Note

Range & interquartile range

What is the range?

• The range is the difference between the highest value and the lowest value

  • range = highest - lowest

    • For example, the range of 1, 2, 5, 8 is 8 - 1 = 7

• It measures how spread out the data is

  • Ranges of different data sets can be compared to see which is more spread out

  • The range of a data set can be affected by very large or small values

• Be careful with negatives

  • The range of -2, -1, 0, 4 is 4 - (-2) = 6

What are quartiles?

• The median splits the data set into two parts

  • Half of the data is less than the median

  • Half of the data is greater than the median

• Quartiles split the data set into four parts

  • The lower quartile (LQ) lies a quarter of the way along the data (when in order)

    • One quarter (25%) of the data is less than the LQ

    • Three quarters (75%) of the data is greater than the LQ

  • The upper quartile (UQ) lies three quarters of the way along the data (when in order)

    • Three quarters (75%) of the data is less than the UQ

    • One quarter (25%) of the data is greater than the UQ

How do I find the quartiles?

• STEP 1
  Write the data in numerical order

• STEP 2
  Use the median to divide the data set into lower and upper halves

  • If there are an even number of data values, then

    • the first half of those values are the lower half,

    • and the second half are the upper half

    • All of the data values are included in one or other of the two halves

  • If there are an odd number of data values, then

    • all the values below the median are the lower half

    • and all the values above the median are the upper half

    • The median itself is not included as a part of either half

• STEP 3
  Find the medians of the two halves

  • The lower quartile is the median of the lower half of the data set

  • The upper quartile is the median of the upper half of the data set

What is the interquartile range (IQR)?

• The interquartile range (IQR) is the difference between the upper quartile (UQ) and the lower quartile (LQ)

  • Interquartile range (IQR) = upper quartile (UQ) - lower quartile (LQ)

• The IQR measures how spread out the middle 50% of the data is

  • The IQR is not affected by extreme values in the data