Basic Descriptive Basic Descriptive StatisticsStatistics

Dr. YehDr. Yeh

Why?Why?

Descriptive statistics do just that: Descriptive statistics do just that: Describe Data!Describe Data!

What we’ll cover in this slidecastWhat we’ll cover in this slidecast– Mean (average)Mean (average)– MedianMedian– ModeMode– RangeRange

MeanMean

Fancy FormulaFancy Formula

µ = µ = X/NX/N

MeanMean

Fancy FormulaFancy Formula

µ = µ = X/NX/N

What this means: What this means: add up all your add up all your data, then divide data, then divide by the number of by the number of data pointsdata points

MeanMean

Sample data:Sample data:

98cm98cm

76cm76cm

82cm82cm

54cm54cm

90cm90cm

MeanMean

Sample data:Sample data:

98cm98cm

76cm76cm

82cm82cm

54cm54cm

90cm90cm

How to calculate:How to calculate:

98+76+82+54+90 = 98+76+82+54+90 = 400cm400cm

MeanMean

Sample data:Sample data:

98cm98cm

76cm76cm

82cm82cm

54cm54cm

90cm90cm

How to calculate:How to calculate:

98+76+82+54+90 = 98+76+82+54+90 = 400cm400cm

400cm/5 = 80cm400cm/5 = 80cm

MeanMean

Sample data:Sample data:

98cm98cm

76cm76cm

82cm82cm

54cm54cm

90cm90cm

How to calculate:How to calculate:

98+76+82+54+90 = 98+76+82+54+90 = 400cm400cm

400cm/5 = 80cm400cm/5 = 80cm

MedianMedian

The median is the middle data point The median is the middle data point in a setin a set

To determine the median, sort the To determine the median, sort the data from smallest to largest and data from smallest to largest and find the middle data pointfind the middle data point

MedianMedian

Sample data:Sample data:

98cm98cm

76cm76cm

82cm82cm

54cm54cm

90cm90cm

MedianMedian

Sample data:Sample data:

98cm98cm

76cm76cm

82cm82cm

54cm54cm

90cm90cm

Rearranged Data:Rearranged Data:

54cm54cm

76cm76cm

82cm82cm

90cm90cm

98cm98cm

MedianMedian

Sample data:Sample data:

98cm98cm

76cm76cm

82cm82cm

54cm54cm

90cm90cm

Rearranged Data:Rearranged Data:

54cm54cm

76cm76cm

82cm82cm

90cm90cm

98cm98cm

MedianMedian

If there is an even number of data, If there is an even number of data, there will be two middle points.there will be two middle points.

To find the median, take the average To find the median, take the average of those two data.of those two data.

MedianMedian

Sample Data:Sample Data:

4ml4ml

8ml8ml

12ml12ml

2ml2ml

MedianMedian

Sample Data:Sample Data:

4ml4ml

8ml8ml

12ml12ml

2ml2ml

Rearranged Data:Rearranged Data:

2ml2ml

4ml4ml

8ml8ml

12ml12ml

MedianMedian

Sample Data:Sample Data:

4ml4ml

8ml8ml

12ml12ml

2ml2ml

Rearranged Data:Rearranged Data:

2ml2ml

4ml4ml

8ml8ml

12ml12ml

4 + 8 = 12ml4 + 8 = 12ml

12/2 = 6ml12/2 = 6ml

ModeMode

The mode is the most frequently The mode is the most frequently occurring data point.occurring data point.

To find the mode, arrange the data To find the mode, arrange the data from smallest to largest, and then from smallest to largest, and then determine which amount occurs determine which amount occurs most often.most often.

ModeMode

Sample Data:Sample Data:

20g20g 23g23g

30g30g 30g30g

22g22g 27g27g

25g25g 20g20g

23g23g 24g24g

23g23g 25g25g

20g20g 23g23g

ModeMode

Sample Data:Sample Data:

20g20g 23g23g

30g30g 30g30g

22g22g 27g27g

25g25g 20g20g

23g23g 24g24g

23g23g 25g25g

20g20g 23g23g

Rearranged Data:Rearranged Data:

20g 20g 20g20g 20g 20g

22g22g

23g 23g 23g 23g23g 23g 23g 23g

24g24g

25g 25g25g 25g

27g27g

30g 30g30g 30g

RangeRange

The range is the distance between The range is the distance between the smallest and largest data point.the smallest and largest data point.

To calculate, determine the smallest To calculate, determine the smallest data point and the largest data point, data point and the largest data point, then subtract the smallest from the then subtract the smallest from the largest.largest.

RangeRange

Sample data:Sample data:

98cm98cm

76cm76cm

82cm82cm

54cm54cm

90cm90cm

Rearranged Data:Rearranged Data:

54cm54cm

76cm76cm

82cm82cm

90cm90cm

98cm98cm

RangeRange

Sample data:Sample data:

98cm98cm

76cm76cm

82cm82cm

54cm54cm

90cm90cm

Rearranged Data:Rearranged Data:

54cm54cm

76cm76cm

82cm82cm

90cm90cm

98cm98cm

98cm – 54cm = 98cm – 54cm = 44cm44cm

RecapRecap

Mean, Median, Mode, and Range Mean, Median, Mode, and Range “describe” the data.“describe” the data.

AcknowledgementsAcknowledgements

American Chemical Society. (2006). American Chemical Society. (2006). Chemistry in the community: Chemistry in the community: ChemComChemCom (5 (5thth ed). New York: W.H. ed). New York: W.H. FreemanFreeman