Unit 3: Averages and Variations Part 3 Statistics Mr. Evans

Focus Points Interpret the meaning of percentile scores Compute the median, quartiles, and five-number summary Make a box-and-whisker plot. Interpret the results Describe how a box-and-whisker plot indicates spread of data around the median

Pth Percentile For whole numbers p (where 1 ≤ P ≤ 99 ), the Pth percentile of a distribution is a value such that P% of the data fall at or below it.

Guided Exercise #1 If you score was at the 89 th percentile, what percentage of scores are at or below yours? 89% of the data falls at or below 11% of data falls above

Quartiles

Procedure to Compute Quartiles 1.Order the data from smallest to largest 2.Find the median. This is the 2 nd quartile 3.The first quartile is the median of the lower half of the data; a)It is the median of the data falling below the position (and not including ) 4.The third quartile is the median of the upper half of the data; 5.It is the median of the data falling above the position (and not including

IQR

Guided Exercise #2 The cost of Ice Cream bars. Find the quartiles and the Interquartile Range IQR = = , 0.17, 0.18, 0.20, 0.25, 0.33, 0.33, 0.35, 0.37, 0.38, 0.40, 0.47, 0.50, 0.50, 0.50, 0.63, 0.84, 0.97, 0.97, 0.99, 1.00, 1.03, 1.07, 1.07, 1.08, 1.23, 2.07 Q1 Q3 Q2

Guided Exercise #2 The cost of Ice Cream bars. Find the quartiles and the Interquartile Range IQR = 319 – 182 = 137 Q1 = 182 Q2 = Q3 = 319

Five Number Summary

Box-and-Whisker Plot The five number summary creates a graphic sketch of data called a box-and-whisker plot.

How to Construct a Box-and-Whisker Plot 1.Draw a vertical scale to include the lowest and highest data values. 2.To the right of the scale draw a box from Q1 and Q3 3.Include a solid line through the box at the median level 4.Draw solid lines, called whiskers, from Q1 to the lowest value and Q3 to the highest value.

Guided Exercise #3 Write the five number summary and draw box-and-whisker plots for both sets of data from exercise # , 0.33, 0.50, 1.00, , 182, 221.5, 319, 439