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EMA104 Mod 1.1 - Introduction to Statistics.pptx
- 1. Introduction to Statistics EMA104 Module 1.1
- 2. • Statistics is the art of learning from data. It is concerned with the collection of data, its subsequent description, and its analysis, which often leads to the drawing of conclusions. • In other situations, data are not yet available; in such cases statistical theory can be used to design an appropriate experiment to generate data. The experiment chosen should depend on the use that one wants to make of the data. • Example!
- 3. Data and Probability Models • Descriptive statistics is the part of statistics concerned with the description and summarization of data • Inferential statistics is concerned with the drawing of conclusions • To be able to draw logical conclusions from data, we usually make some assumptions about the chances (or probabilities) of obtaining the different data values. The totality of these assumptions is referred to as a probability model for the data
- 4. Populations and Samples • Population – total collection of elements • The population is often too large for us to examine each of its members, and therefore has to be subdivided.. • Sample – subgroup of a population • If the sample is to be informative about the total population, it must be, in some sense, representative of that population.
- 5. Describing Data Sets • A data set having a relatively small number of distinct values can be conveniently presented in a frequency table. • Example, Table 2.1 is a frequency table for a data set consisting of the starting yearly salaries (to the nearest thousand dollars) of 42 recently graduated students of engineering. It shows that the lowest starting salary of $57,000 was received by four of the graduates, whereas the highest salary of $70,000 was received by a single student. The most common starting salary was $62,000, and was received by 10 of the students.
- 6. • Data from a frequency table can be graphically represented by a line graph that plots the distinct data values on the horizontal axis and indicates their frequencies by the heights of vertical lines
- 7. • When the lines in a line graph are given added thickness, the graph is called a bar graph.
- 8. • Another type of graph used to represent a frequency table is the frequency polygon, which plots the frequencies of the different data values on the vertical axis, and then connects the plotted points with straight lines.
- 9. Relative Frequency • Consider a data set consisting of n values. If f is the frequency of a particular value, then the ratio f/n is called its relative frequency. • Relative frequency of a data value is the proportion of the data that have that value. • You can also use a pie chart to represent this data with each frequency representing a percentage of the whole pie.
- 10. Grouped Data • For some data sets, the number of distinct values is too large. It is useful to divide the values into groupings, or class intervals, and then plot the number of data values falling in each class interval. • It is common, although not essential, to choose class intervals of equal length. • The endpoints of a class interval are called the class boundaries. • The example adopts the left-end inclusion convention, which stipulates that a class interval contains its left-end but not its right-end boundary point. Thus, for instance, the class interval 20–30 contains all values that are both greater than or equal to 20 and less than 30.
- 12. • A bar graph plot of class data, with the bars placed adjacent to each other, is called a histogram.
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- 18. • The mean, median, and mode are measures of central tendency that are most widely used in the field of descriptive statistics. All the measures provide a different view of the center of the data and ensures that the information is well summarized and interpreted. • In which situations is it best to use mean, median, or mode?
- 19. To be continued