Statistics: Page 6Interquartile Range and Five Number Summary

The Interquartile Range (IQR)

• The Interquartile Range is the spread of the middle 50% of a dataset.

• Calculation of IQR:

  • Subtract the first quartile (Q1) from the third quartile (Q3).

  • Formula: IQR = Q3 - Q1

Five Number Summary

• The Five Number Summary provides five key values that summarize a dataset:

  • Minimum (Min)

  • First Quartile (Q1)

  • Median (Q2)

  • Third Quartile (Q3)

  • Maximum (Max)

Example Data (Sorted)

• Dataset for analysis:

  • {48, 52, 57, 61, 64, 76, 77, 81, 85, 88}

• Calculating the Five Number Summary:

  • Min: 48

  • Max: 88

  • Lower Half: {48, 52, 57, 61, 64}

    • This set will be used to determine Q1 and Q2.

  • Upper Half: {76, 77, 81, 85, 88}

    • This set will be used to determine Q3.

Quartiles Calculations

• Q1: The first quartile (Q1) is calculated as follows:

  • Q1 = 57

• Q2: The median (Q2) is calculated as follows:

  • Median (Q2) = 72

• Q3: The third quartile (Q3) is calculated as follows:

  • Q3 = 81

Summary of Calculations

• Interquartile Range Calculation:

  • IQR = Q3 - Q1

  • IQR = 81 - 57 = 24

Variability Measures

• Range:

  • Range = Max - Min

  • Range = 88 - 48 = 40

• Resistance to Outliers:

  • IQR is considered more resistant to outliers compared to the Mean and Standard Deviation.

  • In statistical analysis, utilizing the IQR instead of Mean and Standard Deviation is advisable when outliers are present in the data.