Lesson 2 Central Position

Lesson 2 Central Position - Data Description 1 Measure of...

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Unformatted text preview: Data Description 1. Measure of Central Tendency 2. Measure of Position 3. Measure of Variability 4. Measure of Shape Measure of Central Tendency- Deals with the three measures of central tendency: Mean Median Mode The measures of central tendency show the location or position of a particular data in a given set of distribution. Measure of Central Tendency for Ungrouped Data MEAN – is the average of all the data. This is the most commonly used measure of location and considered to be the most reliable. Used for ratio data. Affected by extreme values. population mean sample mean where N - total number of observations in the population n – total number of observations in the sample x – is an observation in the set μ = x i 1 N ∑ N x __ = x i 1 n ∑ n Median – the value that divides the distribution into two equal parts; middle value of the distribution. This measure is not affected by extreme values. Can be used for ordinal, interval and ratio data. Obtained by arranging the data in the ascending or descending order. For odd number of observations, the median corresponds to the middle value. For even number of observations, the median is the average of the two middle values. That is, Mode, – is the most frequent data in the distribution. This is the only measure of central tendency that can be used for nominal data. Not sensitive to extreme values ˜ x = x n + 1 2 when n is odd x n 2 + x n 2 + 1 2 when n is even ˆ x Measure of Central Tendency for Grouped Data Mean: A1. Long Method A2. Coding Method A3. Short/Deviation Method x = fx ∑ n x = A + C ∑ fu n x = A + fd ∑ n Where: A - is the class mark of the assumed mean class C - is the class width n - is the number of observations d - is the deviation f - is the frequency u - is the unit code Median : A positional measure defining the middlemost value in the distribution. where cf< - is the less than cumulative frequency of the class preceding the median class C - is the class width ˜ x = L Md + C n 2- cf < ( 29 f Md L Md is the lower class boundary of the median class f Md- is the frequency of the median class Mode:...
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Lesson 2 Central Position - Data Description 1 Measure of...

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