chapter3m211

# chapter3m211 - Math 211 Statistics Introduction to Chapter...

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Math 211 Introduction to Statistics Chapter III The Measures of Central Tendency Index (subscript) Notation: Let the symbol i X (read ‘ X sub i ) denote any of the N values 1 2 , ,..., N X X X assumed by a variable X . The letter i in i X ( 29 1,2,. .., i N = is called an index or subscript. The letters , , , or j k p q s can also be used. Summation Notation: 1 2 1 .... N i N i X X X X = = + + + å Example : 1 1 2 2 1 .... N N N i X Y X Y X Y X Y = = + + + å ( ) 1 2 1 2 1 1 .... .... N N i N N i i i aX aX aX aX a X X X a X = = = + + + = + + + = å å , a Î ¡ Averages (Measures of Central Tendency) The average of a set of numbers is the value which best represents it. There are three different types of averages. Each has advantages and disadvantages depending on the data and intended purpose. Mean This is also known as the arithmetic mean. It is found by dividing the sum of the set of numbers with the actual number of values and defined as 1 2 1 ... N i N i X X X X X X N N N = + + + = = = Example : Find the mean of 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. Sum of values: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55 Number of values = 10 Mean of values= X = 55 / 10 = 5.5 Note: If the numbers 1 2 , ,..., k X X X occur 1 2 , ,..., k f f f times respectively, (occur with frequencies 1 2 , ,..., k f f f ), the arithmetic mean is, 1 k i i i f X X N = = where 1 k i i N X = = is the total frequency. 1

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Sonuç Zorlu Lecture Notes Example : The grades of a student on six examinations were 84,91,72,68,91, and 72. Find the arithmetic mean. The arithmetic mean ( ) ( ) ( ) ( ) 1 1 84 2 91 2 72 1 68 79.67 1 2 2 1 k i i i f X X N = + + + = = = + + + å Example : If 5,8,6 and 2 occur with frequencies 3,2,4 and 1 respectively, the arithmetic mean is 3(5) 2(8) 4(6) 1(2) 57 5.7 3 2 4 1 10 X + + + = = = + + + The Weighted Arithmetic Mean The weighted arithmetic mean of a set of N numbers 1 2 , ,..., N X X X is defined as 1 1 2 2 1 1 2 1 ... ... N i i k k i k k i i w X w X w X w X X w w w w = = + + + = = + + + å å where j w represents the weight of the th j value. Example: If a final examination is weighted 4 times as much as a quiz, a midterm examination 3 times as much as a quiz , and a student has a final examination grade of 80, a midterm examination grade of 95 and quiz grades of 90, 65 and 70, the mean grade is ( ) ( ) ( ) ( ) ( ) 1 90 1 65 1 70 3 95 4 80 830 83 1 1 1 3 4 10 X + + + + = = = + + + + . Properties of the Arithmetic Mean
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## This note was uploaded on 08/12/2011 for the course AS 211 taught by Professor Yuceltandogdu during the Spring '11 term at Eastern Mediterranean University.

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chapter3m211 - Math 211 Statistics Introduction to Chapter...

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