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Statistics 3090

by: Hannah Stephens

Statistics 3090 Stat 3090-005

Hannah Stephens

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These notes cover week 3 of notes and notes from the homework assignment!
Introductory Business Statistics
Paul J. Cubre
Class Notes
Statistics 3090, Intro to Business Statistics, Clemson University
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This 4 page Class Notes was uploaded by Hannah Stephens on Friday January 22, 2016. The Class Notes belongs to Stat 3090-005 at Clemson University taught by Paul J. Cubre in Spring 2016. Since its upload, it has received 62 views. For similar materials see Introductory Business Statistics in Statistics at Clemson University.

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Date Created: 01/22/16
Ch.$2$Defenitions$ $ Confounding$Variable—Variable$that$was$not$controlled$or$accounted$for$by$the$ researcher$and$damages$the$integrity$of$the$experiment.$ $ Descriptive$Statistics—Focuses$on$exploratory$methods$for$examining$data$$ $ Inferential$Statistics—Develops$theories$to$test$the$hypothesis$using$data$collected$ from$an$experiment$to$make$formal$conclusions$about$a$population$or$parameter.$ $ Procedure:$$The$DecisionEMaking$Method$ 1. Clearly$define$the$problem$and$any$influential$variables.$ 2. Decide$upon$objectives$$and$decision$criteria$for$choosing$a$solution.$ 3. Create$alternative$solutions.$ 4. Compare$alternatives$using$the$criteria$est.$in$second$step.$ 5. Implement$the$chosen$alternative.$ 6. Check$the$results$to$make$sure$the$desired$results$are$achieved.$ $ Response$Variable—The$variable$of$interest$in$an$experiment.$$ $ Explanatory$Variable—Variable$that$affects$the$variable$of$interest$(response$ variable)$in$an$experiment.$ $ Placebos—Fake$treatments$ $ Double$Blind$Study—Study$where$neither$the$evaluators$of$the$subjects$are$told$if$ they$are$the$treatment$group$or$the$control$group.$ $ Level$of$Measurement—The$quality$of$data$ $ Nominal$Data—Data$that$represents$whether$a$variable$possesses$some$ characteristic$ $ i.e.$Sex$(male$or$female)$and$hair$color$(blonde,$brunette,$or$redhead)$ $ Ordinal$Data—Represents$categories$that$have$some$associated$order.$ $ i.e.$Have$the$property$of$ordinality$(or$ranking)$ $ Interval$Data—Data$that’s$ordered$and$the$arithmetic$difference$is$meaningful.$ $ i.e.$Difference$between$48$and$45$degrees$is$the$same$as$the$difference$ between$73$and$70$degrees$(3$degrees).$ $ Ratio$Data—Similar$to$interval$data,$however$it$has$a$meaningful$zero$point$and$the$ ratio$of$two$points$is$meaningful.$ $ i.e.$Operations$of$addition,$subtraction,$multiplication,$and$division$are$ reasonable$on$ratio$data.$ $ Qualitative$Data—Measurements$that$can$change$in$kind,$but$not$in$degree.$$ Measured$on$the$nominal$and$ordinal$scales.$$Usually$labels$or$descriptions.$Do$not$ have$naturally$occurring$numerical$values.$ $ i.e.$Gender$(M/F),$Occupation,$eye$color$ $ Quantitative$Data—Measurements$that$change$in$magnitude$from$trial$to$trial$ where$some$order$or$ranking$can$be$used.$$Can$be$measured$using$a$numerical$ scale.$ $ i.e.$Number$of$students$in$a$class,$number$of$dependents$claimed$on$a$tax$ return,$number$of$fans$at$a$sporting$event,$time$it$takes$to$complete$a$task$ $ Discrete$Data—Data$in$which$the$observations$are$restricted$to$a$set$of$values$(such$ as$1,2,3,4)$that$possesses$gaps.$$Can$assume$decimal$values.$ $ Continuous$Data—Data$that$can$take$on$any$value$within$some$interval$$ $ $ Statistics  Ch.  2  Notes   • Bar  Charts—Display  where  the  length  of  a  bar  corresponds  to  the  frequency   or  number  of  corresponds  to  the  frequency  or  number  of  observations  in  a   category.   • Pie  Charts—Slice  is  proportional  to  the  amount  in  each  category   • Relative  Frequency—The  proportion  and  is  calculated  by  relative  frequency   (#  in  the  class)          #  Total               • Cumulative  Frequency—Sum  of  frequencies  of  a  particular  class  and  all   preceding  classes.   • Cumulative  Relative  Frequency—Make  the  cumulative  frequency  relative       Ex.  Assets  of  10  largest  insurance  companies  in  billions:  148.4,  110.8,  55.6,  52.4,   50.4,  42.7,  41.7,  36.3,  35.7,  35.7     Assets   Frequency   Relative  Frequency   Cululative  Frequency   Cumulative  Relative  Frequency   Column1   $30-­‐$59   8   8/10=0.8   8   8/10=0.8   $60-­‐$89   0   8   8/10=0.8     $90-­‐$119   1   1/10=0.1   9   9/10=0.9     $120-­‐$149   1   1/10=0.1   10   10/10=1           • Histogram—A  bar  graph  of  frequency  or  relative  frequency       Algorithm   1. Determine  the  number  of  classes.     2. Find  the  smallest  and  largest  value   3. Class  Width=  largest-­‐smallest   #  of  classes   4. First  class  is  usually  the  first  class  with  the  smallest  number  and  starting  at  a   multiple  of  the  class  width   5. Find  class  boundaries  are  the  average/midpoint  between  two  classes   a. Lower  class  boundary<x<upper  class i boundary   6. Calculate  the  frequency  or  relative  frequency   7. Create  a  bar  graph   **Class  boundaries  are  sometimes  called  cut  points.  Classes  are  sometimes  called   bins.     • Ordered  Array—List  of  all  data  points  in  order   o Rank  Order:    Increasing  order   o Reverse  Rank  Order:    Decreasing  order   • Dot  Plot—Graph  where  each  data  point  is  a  point  above  a  horizontal  axis   (usually  a  number  line)  if  multiple  entries  have  the  same  value  they  are   stacked.   • Probability  Distribution—Assigns  a  probability  to  a  set  of  possible  outcomes   • Symmetric  Distribution—If  one  were  to  draw  a  line  down  the  middle  of  the   distribution  the  two  sides  would  mirror  each  other.   • Skewed  (asymmetrical)  Distribution—Not  symmetric  or  a  group  of   observation  that  are  not  equal  on  both  sides   1. Left  Skewed—Left  side  is  longer   2. Right  Skewed—Right  side  is  longer   • Unimodal—Distribution  has  each  one  “peak”   • Bimodal—Has  exactly  two  “peaks”   • Multimodal—Has  more  than  one  “peak”   How  to  find  the  “center”  of  data?     Suppose  you  have  2  values:    a  and  b,  what  is  the  center?       -­‐Have  to  take  the  avg=  a+b                      2     • Mode—The  value  that  occurs  most  frequently     o Not  necessarily  unique   o One  mode  is  unimodal,  two  is  bimodal,  at  least  two  is  multimodal     • Mean—The  average   th 1. Sample  Mean—Where  X is  the  i i  a  point  in  a  sample.       2. Population  Mean—Where  N  is  the  number  of  elements  in  the   population.   **Aside—Sigma  (Σ)  notation.    Means  add  up  things.     th 3. Weighted  Mean—Suppose  the  i  observation  is  given  a  weight  w.   i 4. Trimmed  Mean—Ignores  equal  percentages  of  the  highest  and   lowest  data  points.   • Median—Data  value  in  the  center  of  an  ordered  list   • Outlier—Data  points  that  are  extremely  small  or  large  relative  to  the  data  set   • Resistant—Statistics  not  affected  by  outliers  are  called  resistant        


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