Topic 4 _Measures of Dispersion.pdf

Topic 4 _Measures of Dispersion.pdf - Measures of...

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Measures of Dispersion Topic 4: Chapter 4
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Why measures of dispersion? n Measures of central tendency give us a numerical center of a distribution – these are measures of location. n Knowing only the center of the distribution is fairly limited n Say that we find that the mean number of times Americans attend religious services a year is 12. We can’t tell if most people attend religious services around 12 times a year, or if a lot of people attend religious services with many different frequencies, and this averages out to 12.
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Why measures of dispersion? (contd.) n Measures of dispersion estimate the spread or variability of a distribution around the center- they indicate a range of variation or average differences among the scores of a frequency distribution. n What does the above remind you of in the context of the discussion on the choice of the measure of central tendency? n We are less familiar with such concepts in our daily lives although we do hear/see of reports such as the temperature forecast ranging between 65-70 degree Fahrenheit. n Read Box Using Statistics, page 91.
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Why measures of dispersion? (contd.) n For example, both these distributions could have a mean of 12, but vary greatly in their variability n The degree to which the responses spread out varies greatly. n See Figure 4.1, page 92 for yet another example.
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Why measures of dispersion? n So, therefore in addition to what is the typical numerical value of the frequency distribution we also need to know the typical-ness of that measure of central tendency. In other words we need to ask - are lot of people like this or is it the summation of a wide range of responses? n This indication of the ‘typical-ness’is called a measure of ‘dispersion’, also sometimes called as ‘variability’, ‘spread’, ‘width’.
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Various measures of dispersion n Variation Ratio n Index of Diversity n Index of Qualitative Variation – is the only measure for nominal level variables. (See Box ‘Statistics in Everyday Life’ – page 95 n Range n Interquartile Range n Quartile Deviation n Mean Deviation n Variance/Standard Deviation n Note : We will be studying the ones in written in color blue.
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Range n Difference in the highest and lowest score in the distribution: n Range = Highest Score - Lowest Score n Range is denoted by ‘R’. n Range evidently is a easy measure to compute. But what is a possible disadvantage of using range as a measure?
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Range (contd.) n Problem is, this only involves two scores, so it doesn't tell us much about the variability of most scores; n for example, take two distributions; n 1,1,2,2,3 and 1,1,2,2,50 n these distributions are very similar, with only one score different. But, the highest and lowest score of these distributions are very different.
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