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Math 1530 Chapter 2 Notes

by: DeAnna Barbour

2

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8

Math 1530 Chapter 2 Notes MATH 1530 L10

DeAnna Barbour
ETSU

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COURSE
Prob/Stat Non-Calculus
PROF.
Masum
TYPE
Class Notes
PAGES
8
WORDS
CONCEPTS
math1530, ETSU1530L10, noncalculus
KARMA
25 ?

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This 8 page Class Notes was uploaded by DeAnna Barbour on Tuesday September 13, 2016. The Class Notes belongs to MATH 1530 L10 at East Tennessee State University taught by Masum in Fall 2016. Since its upload, it has received 2 views. For similar materials see Prob/Stat Non-Calculus in Math at East Tennessee State University.

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Date Created: 09/13/16
You can interpret a histogram with  1) Shape  2) Center 3) Spread To measure the center we need to measure: ➔ Mean ➔ Median ➔ Mode All depending on what kind of data is recorded  For a symmetric graph the center is:  Mean and Median and they are equal For a Right Skewed graph the center is:  Mean is to the right and Median is centered For Left Skewed graph the center is: Mean to the left and the median is centered Mean: algebraic average  7, 8  7 + 8 = 15 ➗ 2 ( total number of data ) 7.5 Mean (summation symbol): ∑x 一 # of data ∑x 一 n ∑ = summation (named Sigma) 40, 35, 15, 20, 25, 30  ∑ x 40+35+15+20+25+30 ―     =                       ―                          = 27.5 n                       6 Median: middle value of the data   Smallest to largest Largest to smallest (must be in order!!!) 7 9 5 3 16 2  2 3 5   7 9 16          6 = median  EX:Find median and mean:  2 3 5 7 9 200 Mean: 7 = 113   Median: 6 = 6 Mean is not resistant!!! Median is resistant!!! Mode: most frequent data 1 2 3 ; No mode! 22 22 22 24 24 24 26 26 ; 22 & 24 mode  resistant measure: a measure is not affected by outliers Spread: how your data is spread   To find the spread of the data find : ➔ Range ➔ Standard deviation  ➔ Quantiles Range: maximum ­ minimum  20 30 40 40 ­ 20 = 20 Standard Deviation: average distance from the mean  n ­ 1 <<< degrees of freedom  Median formulas: If odd > If even >  Spread of data: 1) Range Maximum ­ minimum  : 2) Standard Deviation (variance)  EX: 2  4  6   1) Find the mean (   )  2) 3) 4) If a standard deviation is zero all of the data is the same. There is only one point on a graph.  Is the standard deviation resistant?  No, it is non­resistant. If the mean changes the standard deviation will increase or  decrease 92 86 73 63 60  Mean = 74.8 92 86 73 63 600 Mean = 182.8  *if the mean is increased the standard deviation will increase  *if you change the numbers but the mean remains the same the standard deviation will remain  the same as well Spread:  3) Quartiles  1. Order in smallest to largest  2. Find the median 6 7 8 9 10 12 14 16 18  Q1 = Median of group 1 = 7.5  Q2 = Median = 10 Q3 = Median of group 2  = 15 Are the quartiles resistant?  No, like the median the quartiles will not change. They rely on the median Five Number Summary:  Minimum Maximum Q1 Q2 Q3 Resistant:  Non­Resistant: Mean Median Standard Deviation  Quartiles Symmetrical  Mean & Median are the same Right Skewed: Median = center Mean = Right Quartiles = Spread  Left Skewed: Median = Center Mean = Left Quartiles = Spread Inter Quartile Range (IQR) : to find Q3­Q1 q3= maximum q1= minimum **To find the outlier use IQR EX: 0 thru 15  ­2 = outlier 16 = outlier 13 = not an outlier To find the outliers: (Q1 ­ 1.5IQR, Q3 + 1.5IQR) EX: (4 ­ 1.5 x 6 , 10 + 1.5 x 6) =(­5 , 19) Five Number Summary: used to draw boxplots  Minimum = 2 Maximum = 200 Q1 = 4 Q2 = 7 Q3 = 10  Teacher Made Notes

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