02Means

# 02Means - Statistical Techniques I EXST7005 Measures of...

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Statistical Techniques I EXST7005 Start here Measures of Central Tendency

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Objective - Hypothesis testing Background We will test primarily means, but also variances Means and other measures of central tendency will be discussed Course Progression
SUMMATION OPERATIONS The symbol Σ will be used to represent summation Given a variable, Yi Representing a series of observations from Y1 (the first observation) to Yn (the last observatio out of "n" observations) The notation Σ Yi represents the sum of all of th Yi values from the first to the last

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Y i i n = 1 This notation represents the summation of all Yi starting at i=1 and ending at i=n
Example of Summation EXAMPLE: A variable "length of Bluegill in centimeters" is measured for individuals capture in a seine. This quantitative variable will be called "Y", and the number of individuals captured will be represented by "n". For this example let n = 4 The variable Yi is subscripted in order to distinguish between the individual fish (i) Y1 = 3, Y2 = 4, Y3 = 1, Y4 = 2

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Example of Summation (continued Summation operation: To indicate that we wish to sum all individuals in the sample (size n) we write Σ Yi = Y1 +Y2 +Y3 +Y4 = 3+4+1+2 = 10 where, n = 4
Sum of Squares To indicate the sum of squared numbers, simpl indicate the square of the variable after the summation notation. = Y12 + Y22 + Y32 + Y42 = 32 + 42 + 12 + 22 = 9 +16 +1 + 4 = 30 where n = 4 this is called the Sum of Squares, and should n be confused with the . ..

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Square of the Sum Σ Yi = 10 The square of the sum is represented as ( Σ Yi)2. Yi)2 = 102 = 100
Measures of Central Tendency a measure of location on a scale The most common measure is called the Arithmetic mean or the " average " the sum of all observations divided by the number of observations. This is calculated as the sum of the values of th variable of interest ( Σ Yi ) divided by the numbe of values summed (n).

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Y Y n i i n = = 1 Calculation of the Mean
Example of Calculation of the Mean for 4 fish lengths we previously determined that Σ Yi = Y1 +Y2 +Y3 +Y4 = 10 where, n = 4 The mean is Σ Yi/n = 10/4 = 2.5

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For a larger sample of fish Yi = 7, 9, 9, 3, 6, 5, 0, 7, 0, 7 n=10 Σ Yi = (7+9+9+3+6+5+0+7+0+7) = 53 The mean is 53 / 10 = 5.3 Y Y n i i n = = = = 1 53 7 + 9 + 9 + 3 + 6 + 5 + 0 + 7 + 0 + 7 10 .
Other measures of central tendency MEDIAN - the central-most observation in a ranked (ordered or sorted) set of observations. If the number of observations is even, take the mean of the center most 2 observations EXAMPLE: for the fish sample used earlier, rank the observations

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## This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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02Means - Statistical Techniques I EXST7005 Measures of...

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