Measures of Dispersion (DP IB Applications & Interpretation (AI)): Revision Note

Quartiles & Range

What are quartiles?

• Quartiles are measures of location

• Quartiles divide a population or data set into four equal sections

  • The lower quartile, Q₁ splits the lowest 25% from the highest 75%

  • The median, Q₂ splits the lowest 50% from the highest 50%

  • The upper quartile, Q₃ splits the lowest 75% from the highest 25%

• There are different methods for finding quartiles

  • Values obtained by hand and using technology may differ

• You will be expected to use your GDC to calculate the quartiles

What are the range and interquartile range?

• The range and interquartile range are both measures of dispersion

  • They describe how spread out the data is

• The range is the largest value of the data minus the smallest value of the data

• The interquartile range is the range of the central 50% of data

  • It is the upper quartile minus the lower quartile
    
    
    

    • This is given in the formula booklet

• The units for the range and interquartile range are the same as the units for the data

Standard Deviation & Variance

What are the standard deviation and variance?

• The standard deviation and variance are both measures of dispersion

  • They describe how spread out the data is in relation to the mean

• The variance is the mean of the squares of the differences between the values and the mean

  • Variance is denoted σ²

• The standard deviation is the square-root of the variance

  • Standard deviation is denoted σ

• The units for the standard deviation are the same as the units for the data

• The units for the variance are the square of the units for the data

How are the standard deviation and variance calculated for ungrouped data?

• In the exam you will be expected to use the statistics function on your GDC to calculate the standard deviation and the variance

• Calculating the standard deviation and the variance by hand may deepen your understanding

• The formula for variance is 

  • This can be rewritten as

• The formula for standard deviation is 

  • This can be rewritten as

• You do not need to learn these formulae as you will use your GDC to calculate these