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Basic Descriptive Statistics. Dr. Yeh. Why?. Descriptive statistics do just that: Describe Data! What we’ll cover in this slidecast Mean (average) Median Mode Range. Fancy Formula µ = X/N. Mean. Fancy Formula µ = X/N. Mean.
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Basic Descriptive Statistics Dr. Yeh
Why? • Descriptive statistics do just that: Describe Data! • What we’ll cover in this slidecast • Mean (average) • Median • Mode • Range
Fancy Formula µ = X/N Mean
Fancy Formula µ = X/N Mean • What this means: add up all your data, then divide by the number of data points
Sample data: 98cm 76cm 82cm 54cm 90cm Mean
Sample data: 98cm 76cm 82cm 54cm 90cm Mean How to calculate: 98+76+82+54+90 = 400cm
Sample data: 98cm 76cm 82cm 54cm 90cm Mean How to calculate: 98+76+82+54+90 = 400cm 400cm/5 = 80cm
Sample data: 98cm 76cm 82cm 54cm 90cm Mean How to calculate: 98+76+82+54+90 = 400cm 400cm/5 = 80cm
Median • The median is the middle data point in a set • To determine the median, sort the data from smallest to largest and find the middle data point
Sample data: 98cm 76cm 82cm 54cm 90cm Median
Sample data: 98cm 76cm 82cm 54cm 90cm Median Rearranged Data: 54cm 76cm 82cm 90cm 98cm
Sample data: 98cm 76cm 82cm 54cm 90cm Rearranged Data: 54cm 76cm 82cm 90cm 98cm Median
Median • If there is an even number of data, there will be two middle points. • To find the median, take the average of those two data.
Sample Data: 4ml 8ml 12ml 2ml Median
Sample Data: 4ml 8ml 12ml 2ml Median Rearranged Data: 2ml 4ml 8ml 12ml
Sample Data: 4ml 8ml 12ml 2ml Rearranged Data: 2ml 4ml 8ml 12ml Median 4 + 8 = 12ml 12/2 = 6ml
Mode • The mode is the most frequently occurring data point. • To find the mode, arrange the data from smallest to largest, and then determine which amount occurs most often.
Sample Data: 20g 23g 30g 30g 22g 27g 25g 20g 23g 24g 23g 25g 20g 23g Mode
Sample Data: 20g 23g 30g 30g 22g 27g 25g 20g 23g 24g 23g 25g 20g 23g Rearranged Data: 20g 20g 20g 22g 23g 23g 23g 23g 24g 25g 25g 27g 30g 30g Mode
Range • The range is the distance between the smallest and largest data point. • To calculate, determine the smallest data point and the largest data point, then subtract the smallest from the largest.
Sample data: 98cm 76cm 82cm 54cm 90cm Range Rearranged Data: 54cm 76cm 82cm 90cm 98cm
Sample data: 98cm 76cm 82cm 54cm 90cm Rearranged Data: 54cm 76cm 82cm 90cm 98cm Range 98cm – 54cm = 44cm
Recap • Mean, Median, Mode, and Range “describe” the data.
Acknowledgements American Chemical Society. (2006). Chemistry in the community: ChemCom (5th ed). New York: W.H. Freeman