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by: YALIN ZHANG

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# MAS 201 Chapter3 classnote.pdf MAS 211

Marketplace > University of Miami > Business > MAS 211 > MAS 201 Chapter3 classnote pdf
YALIN ZHANG
UM
INTRODUCTION TO BUSINESS STATISTICS
Mary McKenry

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Class Note. Chapter 3
COURSE
INTRODUCTION TO BUSINESS STATISTICS
PROF.
Mary McKenry
TYPE
Class Notes
PAGES
6
WORDS
KARMA
25 ?

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This 6 page Class Notes was uploaded by YALIN ZHANG on Saturday February 7, 2015. The Class Notes belongs to MAS 211 at University of Miami taught by Mary McKenry in Winter2015. Since its upload, it has received 246 views. For similar materials see INTRODUCTION TO BUSINESS STATISTICS in Business at University of Miami.

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Date Created: 02/07/15
l a MAS 2x01 r39 1 Chapter 3 Descriptive Statistics Numerical Methods Population parameters Sample statistics 1 Measures of Location Measures of Central Tendency 39 x Mean arithmetic average 1 l EX 5 n o Median the value in the middle of the distribution where 50 of the observations are less than this value and 50 are greater than this value To obtain the median place the data in order and determine the middle observation the location will be at n 1l2 For an even number of observations average the middle two 0 Mode The value that occurs most often Example For a sample of six days the following number of birthday cakes were sold 6 9 7 5 6 3 Determine the measures of central tendency Scanned by CamScanner MAS 201 Chapter 3 Percentiles and Quartiles 39 d a are sprea Percentiles provide information about how the data throughout the distribution f x r ercent o The pth percentile represents the value where at leg 8 PEI p the observations are less than or equal to p an a I to this value percent of the observations are greater than or equa l 7 To obtain the p th percentile Arrange the data in numerical order Determine the location of the percentile by multiplying the percentage as a decimal by the number of observations n v if this position is an integer then average the value with the next one if it isn t an integer round up to obtain an integer this represents the location of the percentile Quartiles are percentiles that are commonly used 2 25th Percentile is the 15 Quartile r it mam 50th Percentile is the 2 Cl Quartile and is also the median I75 r 39 7395th Percentile is the 3quot Quartile 1 Exampie Weekly commissions on the sale of computer equipment vary by the experience of the salesperson and the number of hours they may work The following data was collected for 20 sales persons and has been numerically arranged for ease of discussion 150 200 225 225 250 300 325 400 425 500 525 550 550 575 600 625 625 650 675 700 7 r lt g CW7 L ch 2333 a Determine the following Percentiles 39 c g39 e 39 n 1 20th Percentile kite 4A5 meagrem 7 w 237439 02 5an Niejir owl netLt obi if p V 2 35th Percentile WI 4 H 35 Pee mimeL in 73qu 439 r l 039 2 057 AT 5 quotL A 39k b Determine the 1st and 3rd Quartiles E f 35 s l am be L U 15 1 1 r w r tweequot 3 396 I23 5 U l k 153 2 Scannedhy Camscanner I MAS 201 Chapter 3 239 Measu 39 res 0f Dispersuon or Measures of Variability Flange Rangelargest smallest 77 75 K Mean Absolute Deviation 6 O a 2 r 7 l 23 7 2 i x x v 55quotquot 0 Variance 39 l l O 5 0 Standard Deviation O 0 Coefficient of Variation compares the standard deviation to the mean S l 3 CV 100 3 3 039 CV 100 1 Determine these measures of dispersion for the Cake example V A p g i 25 gt3 5911 7 8 U mbce is I f f Scanned by CamScanner 2 AH we mm 2 saw it MAS 201 gt Chapter 3 41 3 Distribution lea1 l 1 Within 2 and mt damee w i 7 f V o Z scorfrepresents theufer of stndard diet I i mmn 2 2 g S j A observation 2 is from the mean Values are typically within 3 standard dewations of the mean so values less than or 7 F4 greater than 3 are potential outliers Z is also referred to as a 2 r a F CAr standardlzed value quot 2 Z 7 3 woLustiat z x r x 2 e 395 S x p s Z gt5 t as 039 0 Empirical Rule Applies only when the data have a bell shaped distribution Mmt gtithqwit mmquot39 o Apprdxnmately 65 of the observations are within one standard deviation of the mean 0 Approximately 95 of the observations are within two standard deviations of the mean Approximately 997 of the observations are within three standard deviations of the mean Notice the relationship of the last statement to the statement about z scores typically being between 3 and 3 O o Chebyshev s Theorem Appliesto any distribution At leastT 122 of the observations will be within 2 73 standard deviations of the mean where z 3 1 I V I Use the Cake Data with Chebyshev s theorem when 218 7 36 5 2 4E l t DtA l39 2 39 9 6 mm qud i wxorao aa heels 7 a t I 390 W Y Cu r least 6774 of w m t 0 Five 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