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Unformatted text preview: MT139C2.PPT 1 34 32 30 28 26 24 22 20 18 16 8 7 6 5 4 3 2 1 MPG Frequency Example (BPS 1.5) • Data on the Highway Gas Mileage for 1998 Midsize Cars: 25 26 29 24 26 29 30 28 28 29 27 28 23 23 25 26 33 29 26 24 28 26 16 25 30 25 DISTRIBUTION HISTOGRAM Class Count 1617 1 1819 2021 2223 2 2425 6 2627 6 2829 8 3031 2 3233 1 MT139C2.PPT 2 Interpreting Histograms • In Any Graphs of Data, Look for the Overall Pattern and Striking Deviations from that Pattern. An Important Kind of Deviation is an Outlier, an Individual Value that Falls Outside the Overall Pattern. • You Can Describe the Overall Pattern of a Histogram by its Shape, Symmetry, Center, and Spread. Shape: What Does the Histogram Look Like? A Box? A Bell? A Spike? A Plate? Symmetry: Does the Left Side of the Histogram Look Like the Right? Is the Distribution Skewed to One Side? Center: At About What Point Do Half of the Values Lie Above and Half Lie Below? Spread: What is the Range from the Lowest to Highest Value? Between what Two Values Does the Bulk of the Data Fall? MT139C2.PPT 3 34 32 30 28 26 24 22 20 18 16 8 7 6 5 4 3 2 1 MPG Frequency MT139C2.PPT 4 800 700 600 500 400 300 200 SAT MT139C2.PPT 5 Median • The Midpoint of a Distribution, the Number Such that Half the Observations are Smaller and the Other Half are Larger.. • Three Steps to Finding the Median of a Data Set: 1. Sort the Data from Smallest to Largest. 2. If the Number of Observations is Odd, the Median (M) is the Center Observation in the Ordered List. The Location of the Median is (n+1)/2 Observations From the End of the List. 3. If the Number of Observations is Even, the Median (M) is the Average of the Two Center Observations in the Ordered List. The Location of the Median is Again (n+1)/2 From the End of the List. MT139C2.PPT 6 Example (BPS 1.28) • Caesarean Sections by Swiss Doctors (Males): RAW DATA 27 50 33 25 86 25 85 31 37 44 20 36 59 34 28 SORTED DATA 20 25 25 27 28 31 33 34 36 37 44 50 59 85 86 MEDIAN LOCATION n = 15 (15 + 1)/2 = 8 Median is Located 8 Observations From the End of the Ordered List. M = 34 MT139C2.PPT 7 Quartiles • The Three Quartiles of a Distribution are Located Such that One Quarter of the Distribution Falls Below the First Quartile, Another Quarter Falls Between the First and Second Quartiles, Another Quarter Falls Between the Second and Third Quartiles, and the Final Quarter Lies Above the Third Quartile. • To Calculate the Quartiles: 1. Sort the Data from Smallest to Largest and Find the Median (M). This is the Second Quartile. 2. The First Quartile (Q 1 ) is the Median of the Observations that are Less than the Overall Median in the Ordered List. 3. The Third Quartile (Q 3 ) is the Median of the Observations greater the Overall Median in the Ordered List. MT139C2.PPT 8 Example (BPS 1.28) • Caesarean Sections by Swiss Doctors (Males): RAW DATA 27 50 33 25 86 25 85 31 37 44 20 36 59 34 28 SORTED DATA 20 25 25 27 28 31 33 34 36 37 44 50 59 85 86 QUARTILE LOCATIONS n* = 7 (7 + 1)/2 = 4 Q 1 = 27 Q 3 = 50 M = 34 MT139C2.PPTMT139C2....
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This note was uploaded on 06/06/2011 for the course MTH 139 taught by Professor Mikekadar during the Winter '00 term at Moraine Valley Community College.
 Winter '00
 MikeKadar
 Statistics

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