110_lec09to10_distnwithnumbers

# 110_lec09to10_distnwithnumbers - Describing Distributions...

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Describing Distributions with Numbers Median Quartiles Mean Mode Standard Deviation Percentiles

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The median, M is the midpoint of a distribution the number such that ½ the observations are smaller and the other ½ are larger. To find: Order all observations from smallest to largest. If n (sample size) is odd, M is the center observations in the ordered list. Find M by counting (n+1)/2 observations from beginning of list. If n is even, M is the average of the 2 center observations in the ordered list. Again, find M by counting (n+1)/2 observations from beginning of list.
Example 1 – Find the Median. The number of Mark McGuire home-runs in his first 9 major league seasons are: 49 32 33 39 22 42 9 9 39 1) Order data. 9 9 22 32 33 39 39 42 49 2) What is n? Even or odd? - Odd - Position of M is (9+1)/2: 5 th position 3) M = 33

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Example 2 – Find the Median. The number of Mark McGuire home-runs in his first 10 major league seasons are: 49 32 33 39 22 42 9 9 39 52 1) Order data. 9 9 22 32 33 39 39 42 49 52 2) What is n? Even or odd? - Even - Position of M is (10+1)/2: 5.5 position (Between 5 th and 6 th ) 3) M = (33+39)/2 = 36
Quartiles – they divide the observations into quarters: ¼ lie below the 1 st quartile (Q 1 ), ½ lie below the median (Q 2 ), and ¾ lie below the 3 rd quartile (Q 3 ). To calculate the quartiles: Order all observations from smallest to largest and find M. – Q

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## This note was uploaded on 02/16/2011 for the course STAT 110 taught by Professor Johnson during the Spring '07 term at South Carolina.

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110_lec09to10_distnwithnumbers - Describing Distributions...

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