STA301 - Statistics and Probability GDB Solution Spring 2013

by plhr60 Sun Jun 16, 2013 5:07 am

plz GDB solution of sta301

The Graded Discussion Board (GDB) for STA301 will be opened on [b]Monday, June 17, 2013 and will be remained open till[b][i]Tuesday, June 18, 2013[i].

The TOPIC of the GDB will be:
[b][i]“What does dispersion indicate about the data? Why is this of great importance?”

Your comments should NOT exceed from 100-150 words.[/i][/i][/b][/b][/b][/i]

by plhr60 Sun Jun 16, 2013 5:08 am

Measures of dispersion measure how spread out a set of data. It is important to know the amount of dispersion, variation or spread, as data that is more dispersed or separated is less reliable for analytical purposes. Dispersion is depend upon the type of scale used to measure data characteristics that is quantitative or categorical.

Dispersion

The central value like mean is generally used to convey the general behavior of a data set. For example, the average score of the class in a math test hints at the general comfort level of the class in the topic which is tested. But, if two classes have the same average score, can the teacher conclude that the understanding level is same for the two classes? The arithmetic mean does not convey the variations displayed in the individual marks of the students. The teacher needs to have some idea about the spread of the marks of both the classes. Teacher needs some numerical measure of dispersion which would convey how the marks are spread about the central value, the mean in this case.

Dispersion is useful to find the relation between the set of data. Actually, there are two measures of dispersion. First is standard deviation and second is variance. So, we will explain both standard deviation and variance in detail.

Standard Deviation: Standard Deviation can be defined as the measurement of describing the variability of given data set. Standard deviation is also used for measuring the exact value of the number in the given data set. Dispersion is defined as the measurement including the average deviation, variance, and then standard deviation. The standard deviation and the variance are most widely used for measuring the dispersion.

by plhr60 Sun Jun 16, 2013 5:09 am

Dispersion Graph

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Dispersion is a measure of data variability. This influences the confidence that an analyst can have in the representativeness and reliability of central location measures. A dispersion graph describes the relationship between two variables. It gives a simple illustration of how one variable can influence the other. When constructing a dispersion graph, first clearly define the variables that are to be evaluated. Plot data pairs using the horizontal axis for probable cause and using the vertical axis for probable effect. A dispersion graph places individual data values along a number line, thereby representing the position of each data value in relation to all the other data values.

by plhr60 Sun Jun 16, 2013 5:10 am

Significance of Measuring Dispersion
Measures of dispersion are needed for four basic purposes:

(i) To determine the reliability of an average.

(ii) To serve as a basis for the control of the variability.

(iii) To compare two or more series with regard to their variability.

(iv) To facilitate the use of other statistical measures.

A brief explanation of these points is given below:

(i) Measures of variation point out as to how far an average is representative of the mass. When dispersion is small, the average is a typical value in the sense that is closely represents the individual value and it is reliable in the sense that it is a good estimate of the average in the corresponding universe. On the other hand, when dispersion is large the average is not so typical, and unless the sample is very large, the average may be quite unreliable.

(ii) Another purpose of measuring dispersion is to determine nature and cause of variation in order to control the variation itself. In matter of health, variations in body temperature, pulse beat and blood pressure are the basic guides to guides to diagnosis. Prescribed treatment is designed to control their variation. In industrial production efficient operation requires control of quality variation, the cause of which are sought through inspection and quality control programmes. Thus measurement of dispersion is basic to the control of cause of variation. In engineering problems measures of dispersion are often especially important. In social sciences a special problem requiring the measurement of variability is the measurement of “inequality” of the distribution of income or wealth, etc.

(iii) Measures of dispersion enable a comparison to be made of two or more series with regard to their variability. The study of variation may also be looked upon as a means of determining uniformity or consistency. A high degree of variation would mean little uniformity or consistency whereas a low degree of variation would mean great uniformity or consistency.

(iv) Many powerful analytical tools in statistics such as correlation analysis, the testing of hypothesis, the analysis of fluctuations, techniques of production control, cost control, and so on are based on measures of variation of one kind or another.

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by plhr60 Sun Jun 16, 2013 5:11 am

Measures of Dispersion

•While measures of central tendency indicate what value of a variable is (in one sense or other) “average” or “central” or “typical” in a set of data, measures of dispersion (orvariability or spread) indicate (in one sense or other) the extent to which the observed values are “spread out” around that center — how “far apart” observed values typically are from each other and therefore from some average value (in particular, the mean). Thus:

–if all cases have identical observed values (and thereby are also identical to [any] average value), dispersion is zero;

–if most cases have observed values that are quite “close together” (and thereby are also quite “close” to the average value), dispersion is low (but greater than zero); and

–if many cases have observed values that are quite “far away” from many others (or from the average value), dispersion is high.

•A measure of dispersion provides a summary statistic that indicates the magnitude of such dispersion and, like a measure of central tendency, is a univariate statistic.

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A measure of central tendency together with a measure of dispersion gives adequate description of data as compared to use of measure of central tendency only, because the averages or measures of central tendency only describes the balancing point of the data set, it does not provide any information about the degree to which the data tend to spread or scatter about the average value. So Measure of dispersion is an indication of the characteristic of the central tendency measure. The smaller the variability of a given set, the more the values of the measure of central tendency will be representative of the data set.

While measures of central tendency are used to estimate "normal" values of a dataset, measures of dispersion are important for describing the spread of the data, or its variation around a central value. Two distinct samples may have the same mean or median, but completely different levels of variability, or vice versa. A proper description of a set of data should include both of these characteristics.