Measure Of Dispersion

A measure of dispersion is a method of measuring the degree by which numerical data or values tend to spread from or cluster about central point of average.

The most common measures of dispersion are the following

1.  The Range

The simplest measure of dispersion.

Calculated by finding the difference between the greatest and the least values of the data.

Useful since it is the easiest to understand.

Affected by extreme data.

The range of values 1, 2, 4, 6, 9, 11, 15, 25 is 25 – 1 = 24

Ungrouped:

            R = H – L

= UB – LB

= 89.5 – 44.5

= 45

Grouped Data:

            R = UB – LB = Boundaries

Class Intervals	Frequency	Class Boundaries	Class Marks
45 – 49	3	44.5 + 49.5/2	47
50 – 54	4	49.5 + 54.5/2	52
55 – 59	6	54.5 + 59.5/2	57
60 – 64	7	59.5 + 64.5/2	62
65 – 69	10	64.5 + 69.5/2	67
70 – 74	7	69.5 + 74.5/2	72
75 – 79	6	74.5 + 79.5/2	77
80 – 84	4	79.5 + 84.5/2	82
85 – 89	3	84.5 + 89.5/2	87

Measure Of Central Tendency

Mean of a set of data:   

    1) Add all the values together       

    2) Divide by the number of values there are

•  The mean takes the total of all the values and spreads the total out evenly to get an average.

Examples:

•  Stan threw ten sets of three darts at a board.         

    His scores were:

            34, 45, 20, 41, 60, 83, 70, 30, 26, 61    

    Find his mean score.    

            Mean = Total score / Number of values

            = 470 ÷ 10           

            = 47

Stan’s mean score is 47.

Median – the middle value in a set of data.

   •  First put the numbers in numerical order.          

            •  Example: 

                       Find the median of:         

                        a) 7, 6, 2, 3, 1, 9, 5 

            Ordered: 1, 2, 3, 5, 6, 7, 9 

                        Median = 5 

            b) 5, 3, 2, 8, 7, 9

Ordered: 2, 3, 5, 7, 8, 9    

There are 2 numbers in the middle.     

The median is in the middle of these.

There can only be one median.   

            Median = 6

Mode – is the most common value in a set of data.

Find the mode of: 

   a) red, blue, yellow, red, green        

            Mode = red

           

   b)  4, 5, 6, 5, 7, 8, 5      

            Mode = 5     

It is possible to have 2 modes. 

•  E.g. 4, 7, 7, 8, 8, 5       

           Mode = 7, 8

           

It is possible to have no mode. 

 •  E.g. 4, 7, 8, 5, 6, 2

Introduction Of Statistical Data

  Primary data – data you collect

–         Example :

·         Surveys

·         Focus groups

·         Questionnaires

·         Personal interviews

·         Experiments and observational study

  Secondary data – data someone else has collected

–         Example :

·         County health departments

·         Vital Statistics – birth, death certificates

·         Hospital, clinic, school nurse records

·         Private and foundation databases

·         City and county governments

  Qualitative Data - Can be separated into different categories that are distinguished by some nonnumeric                characteristics

•       Deals with descriptions.

•       Data can be observed but not measured.

•       Colors, textures, smells, tastes, appearance, beauty, etc.

•       Qualitative → Quality

   Quantitative Data - Numbers representing counts or measurements

•       Deals with numbers.

•       Data which can be measured.

•       Length, height, area, volume, weight, speed, time, temperature, humidity, sound levels, cost, members,           ages, etc.

•       Quantitative → Quantity

Example 1:  Oil Painting Qualitative data: ·         red/green color, gold frame ·         smells old and musty    ·         texture shows brush strokes of oil paint ·         peaceful scene of the country ·         masterful brush strokes

Example 1:  Oil Painting Quantitative data: ·         picture is 10" by 14” ·         with frame 14" by 18” ·         weighs 8.5 pounds     ·         surface area of painting is 140 sq. in. ·         cost $300

Example 2:  Latte Qualitative data: *robust aroma *frothy appearance * strong taste *glass cup

Example 2:  Latte Quantitative data: *12 ounces of latte *serving temperature 1500 F. *serving cup 7 inches in height *cost $4.95

Example 3:  Freshman Class Qualitative data: *friendly demeanors *civic minded *environmentalists *positive school spirit

Example 3:  Freshman Class Quantitative data: *672 students *394 girls, 278 boys *68% on honor roll *150 students accelerated in mathematics