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.
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.
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
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?
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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• Fall '11
• Gemelli

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