th 50 th median and 75 th percentiles respectively Q1 1 st quartile 25 th

# Th 50 th median and 75 th percentiles respectively q1

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th , 50 th (median), and 75 th percentiles, respectively (Q1) 1 st quartile = 25 th percentile (Q2) 2 nd quartile = 50 th percentile (AKA median) (Q3) 3 rd quartile = 75 th percentile Example: Mishandled Baggage Reports (1990 – 2007) 1990 6.73 1991 5.38 1992 5.87 1993 5.6 1994 5.33 1995 5.18 1996 5.3 1997 4.96 1998 5.16 1999 5.08 2000 5.29 2001 4.58 2002 3.84 2003 4.19 2004 4.91 2005 6.64 2006 6.73 2007 7.03 Sort data lowest to highest (ascending) Finding Q1 (25 th percentile) - Index point – i = P/100 (n)
- Set P = 25 - 25/100 (18) = 4.5 - 4.5 rounded up to 5 - 5 th position in data = 4.96 Finding Q2 (50 th percentile) - Set P = 50 to find index point - 50/100 (18) = 9 - Midpoint b/w 9 and 10 th positions - (5.29 + 5.3) / 2 = 5.295 Finding Q3 (75 th percentile) - Set P = 75 to find index point - 75/100 (18) = 13.5 - 13.5 rounded up to 14 - 14 th position = 5.87 Finding Quartiles with Excel =QUARTILE (array, quart) Array = data range of interest Quart = the “QUART” value QUART QUARTILE RETURNS 0 Minimum Value 1 Q1 2 Q2 3 Q3 4 Maximum Value Inter-quartile Range (IQR) – describes the middle 50% of a range IQR = Q3 – Q1 Represents the span of the IQR (the range in which 50% of the values fall) Box-and-Whisker Plots Box-and-whisker plot – a graphical display showing the relative position of the three quartiles as a box on a number line along with the minimum and maximum values in the data set and any outliers Ex: Number of National Park Visitors Park 1 9.04 Park 2 4.43 Park 3 3.43 Park 4 3.08
Park 5 3.07 Park 6 2.83 Park 7 2.76 Park 8 2.69 Park 9 2.49 Park 10 2.08 Park 11 1.81 Park 12 1.08 Park 13 1.04 Park 14 0.82 Park 15 0.43 Step by Step 1. Determine the 3 Quartiles Q1 (25 th percentile) - 25/100 • 15 = 3.75 - 3.75 rounded up to 4 th position - 4 th position = 1.08 (4 from bottom) Q2 (50 th percentile) - 50/100 • 15 = 7.5 - 8 th position = 2.69 Q3 (75 th percentile - 75/100 • 15 = 11.25 - 12 th position = 3.08 2. Draw Horizontal Number Line that Spans Data Max/Min 3. Draw Box on Number Line Vertical lines for each of the quartile values 4. Determine Outliers Upper Limit = Q3 + 1.5(IQR) Lower Limit = Q1 – 1.5(IQR) IQR = Q3 – Q1 (3.08) – (1.08) = 2 Upper: 3.08 + 1.5(2) = 6.08 Lower: 1.08 – 1.5(2) = -1.92 5. Draw Whiskers Horizontal lines that go to values that are within the upper and lower limits 6. Identify Outliers if Present

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• Fall '12
• Donnelly