📚 Find the quartiles and percentiles for a data set

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A percentile tells approximately what percent of the data are less than a particular data value.

A quartile is any of three numbers that separate a sorted data set into four equal parts.
• The second quartile is the median (the middle number), it cuts the data into half. So it is the same as 50th percentile.
• The first, or lowest quartile is the median of the data values less than the second quartile. It separates the lowest 25% of the data set. So it is the same as 25th percentile.
• The third, or upper quartile is the median of the data values greater than the second quartile. It separates the highest 25% of the data set. So it is the same as 75th percentile.

Here are the hourly pay rates, in dollars, for 17 high-school students with part-time jobs.

11.50, 10.20, 8.00, 8.25, 9.00, 9.15, 9.75, 7.50, 8.00, 12.50, 13.00, 11.25, 10.75, 9.50, 9.25, 9.45, 7.75

a) What are the quartiles for this data set?

b) Damien’s pay is in the 85th percentile for this group. What does the percentile mean? What is Damien’s hourly pay rate?