Business Statistics•1

Methods of presenting DataMethods of presenting Data

Tabular MethodTabular Method Graphical MethodGraphical Method

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Quantitative Data PresentationQuantitative Data Presentation

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OrderedArray

OgivePolygonHistogram

FrequencyDistributions

QuantitativeData

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Data Array

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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

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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

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The table that organizes the data into mutually exclusive classes or categories is called frequency distribution.

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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

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Frequency Distribution

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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

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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

.,

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Frequency Distribution

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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

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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.

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Some definitions

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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.

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Some definitions

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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.

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Some definitions

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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.

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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

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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

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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

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Data Array

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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

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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

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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