MTH302 Short Notes Lectures 23-45

MTH302 Short Notes for Final Term (Chapter 23-45)

STATISTICAL DATA:

Information is collected by government departments, market researchers, opinion pollsters and others.

BASIS FOR CLASSIFICATION:

1. Qualitative: Attributes: sex, religion
2. Quantitative Characteristics: Heights, weights, incomes etc.
3. Geographical: Regions: Provinces, divisions etc.
4. Chronological or Temporal
5. By time of occurrence: Time series

TYPES OF CLASSIFICATION:

There are different types of classifications. One-way One characteristic: Population Two-way Two characteristics at a time Three-way Three characteristics at a time

METHODS OF PRESENTATION:

Different methods of representation are:

Text ”The majority of population of Punjab is located in rural areas.” Semi-tabular Data in rows Tabular Tables with rows and columns Graphic Charts and graphs

TYPES OF GRAPHS:

Column Graphs

Circle Graphs (Sector Graphs) Conversion Graphs Travel Graphs Statistical Graphs Frequency Tables Histograms Frequency distributions Cumulative Distributions

Line graphs are the most commonly used graphs. Here the data of one variable (say Height) is plotted against data of the other variable (say Age).

MEAN:

The most common average is the mean. The mean is used for things like marks and scores (e.g. sport), and is found by adding all the scores and dividing by the number of scores.

Example:

Marks 58 69 73 67 76 88 91 and 74 (8 marks). Sum = 596 Mean = 596/8 = 74.5 Please note that the mean is affected by extreme values.

MEDIAN:

Another typical value is the median. The median is the middle value when the data are arranged in order. The median is easier to find than the mean, and unlike the mean it is not affected by values that are unusually high or low

Example:

Data 3 6 11 14 19 19 21 24 31 (9 values) The median is the middle score, or the mean of the two middle scores, when the scores are placed in order. In the above data there are 9 values. The middle value is 19.

When there is no middle value, the median is obtained by taking the average of the two middle values.

MODE:

The most common score in a set of scores is called the mode. There may be more than one mode, or no mode at all

The mode, or most common value, is 1.

ORGANISING DATA:

There are many different ways of organizing data.

Organizing Numerical Data

Numerical data can be organized in any of the following forms:

The Ordered Array and Stem-leaf Display Tabulating and Graphing Numerical Data Frequency Distributions: Tables, Histograms, Polygons Cumulative Distributions: Tables, the Ogive

Tabulating and Graphing Univariate Categorical Data:

There are different ways of organizing univariate categorical data: The Summary Table Bar and Pie Charts, the Pareto Diagram

Tabulating and Graphing Bivariate Categorical Data:

Bivariate categorical data can be organized as:

Contingency Tables Side by Side Bar charts

GRAPHICAL EXCELLENCE AND COMMON ERRORS IN PRESENTING DATA:

It is important that data is organized in a professional manner and graphical excellence is achieved in its presentation.

Tabulating Numerical Data:

The process of developing frequency distributions is described below.

Step 1: Sort Raw Data in Ascending Order

Data: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

Step 2: Find Range Range: 58 - 12 = 46

Step 3: Select Number of Classes Select the number of classes. (The classes are usually selected between 5 and 15)

Step 4: Compute Class Interval (width) Step 5: Determine Class Boundaries (limits)