Business Statistics 1 Methods of presenting Data Tabular Method Tabular Method Graphical Method...
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Transcript of Business Statistics 1 Methods of presenting Data Tabular Method Tabular Method Graphical Method...
Business Statistics•1
Methods of presenting DataMethods of presenting Data
Tabular MethodTabular Method Graphical MethodGraphical Method
Business Statistics
Quantitative Data PresentationQuantitative Data Presentation
•2
OrderedArray
OgivePolygonHistogram
FrequencyDistributions
QuantitativeData
Business Statistics
Data Array
•3
Data placed in rank order Data placed in rank order
smallest smallest to to largest largest (or (or largestlargest to to smallestsmallest)) ExampleExample
Data in raw form (as collected)
24, 26, 24, 21, 27, 27, 30, 41, 32, 38 Data in ordered array 21, 24, 24, 26, 27, 27, 30, 32, 38, 41
Business Statistics
Presenting Data in Array: An Example
•4
Raw Data: Yards Produced by 30 Carpet Looms
16.2 15.4 16.0 16.6 15.9 15.8 16.0 16.8 16.9 16.8 15.7 16.4 15.2 15.8 15.9 16.1 15.6 15.9 15.6 16.0 16.4 15.8 15.7 16.2 15.6 15.9 16.3 16.3 16.0 16.3
Arrange the data in order array
Business Statistics
Frequency Distribution
•5
The table that organizes the data into mutually exclusive classes or categories is called frequency distribution.
Business Statistics
Frequency distribution Data in raw form Data in raw form
24, 24, 21, 27, 24, 24, 21, 27, 27, 30, 38, 2727, 30, 38, 27
Observations Frequency
21 1
24 2
27 3
30 1
38 1
Business Statistics
Frequency Distribution
•7
Classes Frequency
10 but less than 20 3
20 but less than 30 6
30 – 40 5
40 – 50 4
50 – 60 2
Prices of books sold yesterday at bookshop:
27, 12, 13, 21, 43, 24, 37, 26, 27, 30, 17, 32, 35, 38, 41, 53, 44, 46, 24, 58.
Business Statistics
Constructing a Frequency Distribution
•8
Determination of Range,
R = Highest value- lowest value Determination of number of class. H.G. Struges, K = 1+3.322 logN Determination of class interval, R/K Identify the data for each class by tally mark. Counting tally marks and frequency determination
.,
Business Statistics
Frequency Distribution
•9
Classes Tally Frequency
10 but less than 20 3
20 but less than 30 6
30 – 40 5
40 – 50 4
50 – 60 2
Total 20
Prices of books sold yesterday at bookshop:
27, 12, 13, 21, 43, 37, 26, 27, 30, 17, 32, 35, 38, 41, 53, 44, 46, 24, 58.
Business Statistics
Construct a frequency distributionMarks in Business Statistics of BBA
students are given below:
45,76, 89, 40, 54, 59, 62, 26, 47, 65, 78, 71, 82, 35, 45, 58, 67, 73, 72, 85, 52, 60, 67, 22, 48,50, 38, 57, 65, 78, 76, 73,68, 64, 55.
Construct a frequency distribution.
Business Statistics
Some definitions
•11
Class
In process of constructing frequency distribution, raw data are assigned to some chosen groups of appropriate size. These groups are called classes.
For example 10 -20, 20 -30, 30 - 40 etc are classes.
Business Statistics
Some definitions
•12
Frequency The number of observations or values falling into each group or class is called class frequency or frequency.
For example, 5 observations fall in class 30 – 40. So
The frequency of that class is 5.
Business Statistics
Some definitions
•13
Class limitsEach class is formed by two boundary values. These two values are known as class limits. The smallest value is called lower limit and the upper limit is called upper limit.
For example, For a class 30 – 40, 30 is the lower limit
and 40 is the upper limit.
Business Statistics
Some definitions
•14
Class-width
The size of class is referred to as the class width and is the difference between the two class limits.
For example, Here the class width is 10.
Business Statistics
Some definitionsMid- value
The value which lies in the middle of a class is called mid-value of that class.
For exampleFor class 30 – 40, the mid value is 35. It is obtained by (30+40)/2=35. For class 50 – 60, the mid value is 55.
Business Statistics
Frequency Distribution
Classes Frequency
10 but less than 20 3
20 but less than 30 6
30 – 40 5
40 – 50 4
50 – 60 2
16
Business Statistics
Relative Frequency Distribution
•17
The frequency distribution which presents frequencies in terms of fraction or percentage in each class is called relative frequency distribution. Classes frequency Relative
frequency
10 but less than 20
3 3/20= .15 (15%)
20 – 30 6 6/20= 0.30 (30%)
30 - 40 5 5/20= 0.25 (25%)
40 – 50 4 4/20= 0.20 (20%)
50 - 60 2 2/20= 0.10 (10%)
Total 20
Business Statistics
Cumulative Frequency Distribution
•18
Cumulative frequency distribution is one which used to determine how many or what proportion of the data values are below or above a certain value.Classes Frequency Cumulative
frequency % cumulative
frequency
10 but less than 20 3 3 15% (3/20)
20 – 30 6 9 (3+6) 45% (9/20)
30 – 40 5 14 (3+6+5) 70%
40 – 50 4 18 (14+4) 90%
50 – 60 2 20 (18 +2) 100%
Total 20
Business Statistics
Data Array
•19
1.1. Organizes data to focus on major Organizes data to focus on major featuresfeatures
2.2. Data placed in rank order Data placed in rank order smallest to largest (or largest to smallest)smallest to largest (or largest to smallest)
3.3. Data in raw form (as collected)Data in raw form (as collected)24, 26, 24, 21, 27, 27, 30, 41, 32, 3824, 26, 24, 21, 27, 27, 30, 41, 32, 38
4.4. Data in ordered arrayData in ordered array21, 24, 24, 26, 27, 27, 30, 32, 38, 4121, 24, 24, 26, 27, 27, 30, 32, 38, 41
Business Statistics
Presenting Data in Array: An Example
•20
Raw Data: Yards Produced by 30 Carpet Looms
16.2 15.4 16.0 16.6 15.9 15.8 16.0 16.8 16.9 16.8
15.7 16.4 15.2 15.8 15.9 16.1 15.6 15.9 15.6 16.0
16.4 15.8 15.7 16.2 15.6 15.9 16.3 16.3 16.0 16.3
Data Array: Daily Production in Yards of 30 Carpet Looms
15.2 15.7 15.9 16.0 16.2 16.415.4 15.7 15.9 16.0 16.3 16.615.6 15.8 15.9 16.0 16.3 16.815.6 15.8 15.9 16.1 16.3 16.815.6 15.8 16.0 16.2 16.4 16.9
Business Statistics
Constructing an Ungrouped Frequency Distribution
•21
Raw Data:
15.2 15.2 15.3 15.3 15.3 15.3 15.3 15.4 15.4 15.4 15.4 15.4 15.4 15.4 15.4 15.4 15.4 15.4 15.5 15.5 15.5 15.5 15.5 15.5 15.6 15.6 15.6 15.7 15.7 15.7
Frequency Distribution
Class _15.215.315.415.515.615.7
Tallies _////////// //// / //// ///////
Frequency _
25
1163
3 30
Relative Frequency
0.070.160.370.200.10
0.10 1.00
Cumulative Rel. Freq.
0.070.230.600.800.901.00