Range & Quartiles | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Range & IQR

What are the range and interquartile range (IQR)?

• The three measures of central tendency—mean, median, and mode—indicate what is typical within the data, showing what is approximately in the center.
• The range and interquartile range (IQR) quantify the dispersion of the data.
  • These metrics are applicable exclusively to numerical data.
  • Fortunately, both are straightforward to calculate.

How do I work out the range?

• The range is calculated as the difference between the highest and lowest data values.
  • It indicates the extent of data dispersion.
  • You can recall this as "Hi - Lo."
• There is a potential issue with using the range:
  • Since it takes into account only the highest and lowest values, it can be affected by outliers.
  • These outliers may not accurately reflect the overall spread of the data.

How do I find the quartiles?

• The median divides the data set into two equal parts, positioned halfway along the data.
• Quartiles, as their name implies, split the data set into four equal parts:
  • The lower quartile (LQ) is located one quarter of the way through the data (when ordered).
  • The upper quartile (UQ) is located three quarters of the way through the data.
• The median can also be referred to as the second quartile.
• To find quartiles, first use the median to split the data set into lower and upper halves:
  • Ensure the data is sorted numerically.
• If the data set has an even number of values:
  • The first half consists of the lower values, and the second half consists of the higher values.
  • In this case, all data points are included in one of the two halves.
• If the data set has an odd number of values:
  • The lower half includes all values below the median.
  • The upper half includes all values above the median.
  • The median itself is excluded from both halves.
• The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half.
• Find the quartiles in the same way you would find the median for any data set, focusing only on the lower or upper half accordingly.
• Sometimes you may also see the quartiles given in formula form
  • For n data values:
    • the lower quartile is the
    • the upper quartile is the
  • Using these can save finding the median and splitting the data into two halves

How do I work out the interquartile range (IQR)?

• The interquartile range (IQR) is the difference between the upper quartile (UQ) and the lower quartile (LQ).
  • To calculate the IQR, you must first determine the quartiles.
• The formula for the interquartile range is IQR = UQ - LQ.
• The IQR measures the spread of the middle 50% of the data, making it resistant to the influence of extreme values.
• Conversely, the range of a data set can be impacted by extremely high or low values.