Quantitative Methods -

Business Mathematics

Data Analysis and Interpretation

CONTENT

Basic ConceptsFrequency Distribution

Ungrouped and Grouped Data Relative Frequency Cumulative Frequency

Graphical Depiction of Data Histogram Frequency Polygon Ogive Pie Charts Pareto Chart

Basic Concepts

Population: Collection of persons / objects / items of interest (e.g. Female in India)

Census: Using data from whole population for a given measurement of interest (e.g. % of educated female in India)

Sample: A portion of population (if properly taken, representative of the population) (e.g. 50,000 females selected from various states and various age group)

Parameter: A descriptive measure of population, e.g. Mean income of population

Statistic: A descriptive measure of sample, e.g. Mean income of a sample

Inferential Statistics: From sample data, conclusion is drawn about population. (e.g. mean income of population is Rs. 25,000 inferred from mean income of sample

Frequency Distribution

Ungrouped Data – Raw data (see Table 2.1 of BLACK) Grouped Data – Data organized in Frequency

Distribution (see Table 2.2 of BLACK) Range: Largest No – Smallest No =12.5-1.2 = 11.3 Class Interval – (e.g. 3-Under 5) Class Beginning Point: 3 Class Width: 2 Class Midpoint = 3+ ½*2 = 4 Frequency - # of observations in that class interval Relative Frequency – Proportion of total frequency (i.e.

Individual Class Frequency / Total Class Frequency Cumulative Frequency – Running Freq. till this class

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Data Visualization:Descriptive Charts and Graphs

Ungrouped data: Raw data, or data that have not been summarized in any way.

Frequency distribution: A summary of data presented in the form of class intervals and class frequencies.

Grouped data: Data that have been organized into a frequency distribution.

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Frequency Distribution

Steps in the construction of a frequency distribution1. Determine the range of

the raw data.

2. Determine how many classes a frequency distribution should have.

3. Determine the width of the class interval.

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Frequency Distribution – Key Terms

Class Midpoint: It is the average of the two class endpoints. This value is important, because it becomes the representative value for each class in most group statistics

calculations.Relative Frequency: The proportion of the total frequencies that fall into any given class

interval in a frequency distribution. Cumulative Frequency: A running total of frequencies through the classes of a frequency

distribution.

Problems

Do Problem 1 Chapter 2 BLACK to calculate Frequency distribution, relative frequency, cumulative frequency, etc.

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Graphical Depiction of Data

Histogram: It is a type of vertical bar chart constructed by graphing line segments for the frequencies of classes across the class intervals and connecting each to the X-axis to form a series

of rectangles. Frequency

Polygon: A graph constructed by plotting a dot for the frequencies at the class midpoints and connecting the

dots.

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Graphical Depiction of Data

Ogives: An ogive is a cumulative frequency polygon; plotted by graphing a dot at each class endpoint for the cumulative or de-cumulative frequency value and connecting the dots.

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Graphical Depiction of Data

Problems

Do Problem 2 Chapter 2 BLACK to draw histogram, frequency polygon, Ogive

Do problem 3 Chapter 2 BLACK to draw pie chart Do problem 4 Chapter 2 BLACK Stem and Leaf Chart Do problem 5 Chapter 2 BLACK Pareto Chart Advantages of Stem and Leaf Chart

Raw data preserved (In frequency distribution, it is not preserved)

Easy to see distribution on left and right Advantages of Pareto Principle

ABC analysis to concentrate on important aspects Do Problem 6 Chapter 2 BLACK Scatter Chart