Percentiles:

• The value such that a specified percent of the data is below that value
• Example: If the 80% percentile (P₈₀) = 179, then 80% of the data is below 179.
• We will use = PERCENTILE.INC(array, k) in Excel to determine these values

Quartiles:

• The data can be ‘split’ into four quarters
• Q₁ is the value such that 25% of the data is below this value (=P₂₅)
• Q₂ is the value such that 50% of the data is below this value (=P₅₀)
• Note: Q₂ is also the median
• Q₃ is the value such that 75% of the data is below this value (=P₇₅)
• We will use = QUARTILE.INC(array, quart) in Excel to determine the quartiles

Five Number Summaries

Data can be ‘summarized’ by its five number summary. This summary is used to determine the shape of the data and generate boxplots.

1. Minimum (min) – the minimum value in the data
2. First quartile (Q₁) – the first quartile value
3. Median (Q₂) – the second quartile value
4. Third quartile (Q₃) – the third quartile value
5. Maximum – the maximum value in the data

Generating the five number summary in Excel (video)

Example 11.1.1

Problem Setup: Again, we are working with the 30 students’ heights from BCIT (click here to download as Excel sheet) and see the table of values below. We want to create the five number summary for their heights:

Question: What is the five number summary for the above students’ heights?

Solution: Click here to view the solutions (five number summary) shown in the above video:

Key Takeaways (EXERCISE)

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