Topic 3_Measures of CentralTendency.pdf

Topic 3_Measures of CentralTendency.pdf - Measures of...

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Measures of Central Tendency Topic 3 :Chapter 3
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Till now we know… n Variables have different characteristics (discrete or continuous) and accordingly follow varying levels of measurement – nominal, ordinal, interval-ratio. n The descriptive statistics such as the appropriate frequency distributions and graphical methods which summarize the overall shape of the distribution vary depending on the level of measurement of the variable.
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Measures of central tendency n Measures of central tendency help reduce the huge array of numbers into single digit numbers. n Read Box Using Statistics (page 66) to get an idea of the utility of Measures of Central Tendency. n Measures of central tendency summarize the entire distribution of the scores by describing the most common score ( mode ), the score in the middle case ( median ) or the average or most typical score ( mean ) of the distribution. (See page 67) n The three measures therefore vary in terms of how they define central tendency.
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Measures of central tendency (contd.) n Also, different variables possess different numerical characteristics –the appropriateness of the measure of central tendency depends on the type and level of measurement of the variable. n Note that the three measures for a particular distribution will have the same value only under specific and limited conditions, something that we learn more later in the course.
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Mode n Most frequently occurring value in a group of raw scores or the value of the group that contains the most cases in a grouped data (modal category). n Can be used with nominal, ordinal, or interval-level data. n The only measure of central tendency which can be used for nominal-level data.
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Mode (contd.) n Mode in nominal data – since nominal level data does not have numerical scores, mode is the category with the highest frequency. n Find the mode for the above distribution. n Find the mode in Table 3.1, page 67. Region Frequency Percent Northeast 569 20.1 Midwest 696 24.6 South 1022 36.1 West 545 19.2 Total 2832 100
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Mode (contd.) n Mode in ordinal data with non-numerical categories n How important is religion? n Here the mode is the category ‘somewhat’ and not ‘1518’. Religious Importance Score f Very 4 649 Somewhat 3 1518 Not very 2 612 Not at all 1 191 Total 2970
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Mode (contd.) n Mode for interval –ratio level data n Ungrouped data n what is the mode in the following set of scores?; 58, 65, 82, 82, 90, 98 n what is the mode if the distribution of scores is 58, 65, 82, 82, 90, 90?
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Mode (contd.) n Grouped data n Mode is the single category among the k categories in a distribution (or highest percentage) of observations n Example –find the mode of these 12 scores n Score Frequency n Y 1 =7 Y 7 = 5 2 1 n Y 2 =6 Y 8 = 6 3 2 n Y 3 =3 Y 9 = 7 5 3 n Y 4 =2 Y 10 = 7 6 2 n Y 5 =7 Y 11 = 5 7 4 n Y 6 =5 Y 12 = 3 Mode = ??? n Find the mode in Table 3.3, page 68.
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Mode (contd.) n Grouped data n To take another example of grouped data….
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