Descriptive Statistics - Business Statistics - Homework, Exercises of Business Statistics

Download Descriptive Statistics - Business Statistics - Homework and more Exercises Business Statistics in PDF only on Docsity! Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 1 of 20 DESCRIPTIVE  STATISTICS:  HOMEWORK   Susan Dean and Barbara Illowsky (2012) EXERCISE  1   Twenty-­‐five  randomly  selected  students  were  asked  the  number  of  movies  they  watched  the   previous  week.  The  results  are  as  follows:   a. Find  the  sample  mean,    .   b. Find  the  sample  standard  deviation,  s.   c. Construct  a  histogram  of  the  data.   d. Complete  the  columns  of  the  chart.   e. Find  the  first  quartile.   f. Find  the  median.   g. Find  the  third  quartile.   h. Construct  a  box  plot  of  the  data.   i. What  percent  of  the  students  saw  fewer  than  three  movies?   j. Find  the  40th  percentile.   k. Find  the  90th  percentile.   l. Construct  a  line  graph  of  the  data.   m. Construct  a  stem  plot  of  the  data.   EXERCISE  2   The  median  age  for  U.S.  blacks  currently  is  30.1  years;  for  U.S.  whites  it  is  36.6  years.  (Source:     U.S.  Census).   a. Based  upon  this  information,  give  two  reasons  why  the  black  median  age  could  be  lower   than  the  white  median  age.   b. Does  the  lower  median  age  for  blacks  necessarily  mean  that  blacks  die  younger  than   whites?    Why  or  why  not?   Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 2 of 20 c. How  might  it  be  possible  for  blacks  and  whites  to  die  at  approximately  the  same  age,   but  for  the  median  age  for  whites  to  be  higher?             EXERCISE  3   Forty  randomly  selected  students  were  asked  the  number  of  pairs  of  sneakers  they  owned.    Let   X  =  the  number  of  pairs  of  sneakers  owned.    The  results  are  as  follows:     a. Find  the  sample  mean     b. Find  the  sample  standard  deviation,  ss   c. Construct  a  histogram  of  the  data.     d. Complete  the  columns  of  the  chart.     e. Find  the  first  quartile.     f. Find  the  median.     g. Find  the  third  quartile.     h. Construct  a  box  plot  of  the  data.     i. What  percent  of  the  students  owned  at  least  five  pairs?     j. Find  the  40th  percentile.     k. Find  the  90th  percentile.   l. Construct  a  line  graph  of  the  data.   m. Construct  a  stem  plot  of  the  data.     EXERCISE  4     600  adult  Americans  were  asked  by  telephone  poll,  What  do  you  think  constitutes  a  middle-­‐class   income?    The  results  are  below.    Also,  include  left  endpoint,  but  not  the  right  endpoint.  (Source:     Time  magazine;  survey  by  Yankelovich  Partners,  Inc.)      Note:  "Not  sure"  answers  were  omitted  from  the  results.   Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 5 of 20 a. In  complete  sentences,  describe  what  the  shape  of  each  box  plot  implies  about  the   distribution  of  the  data  collected.   b. Explain  how  it  is  possible  that  more  Americans  than  Germans  surveyed  have  been  to   over  eight  foreign  countries.   c. Compare  the  three  box  plots.    What  do  they  imply  about  the  foreign  travel  of  twenty   year  old  residents  of  the  three  countries  when  compared  to  each  other?             EXERCISE  8   Twelve  teachers  attended  a  seminar  on  mathematical  problem  solving.    Their  attitudes  were   measured  before  and  after  the  seminar.    A  positive  number  change  attitude  indicates  that  a   teacher's  attitude  toward  math  became  more  positive.    The  twelve  change  scores  are  as  follows:     {  3;    8;    -­‐1;    2;    0;    5;    -­‐3;    1;    -­‐1;    6;    5;    -­‐2  }     a. What  is  the  average  change  score?   b. What  is  the  standard  deviation  for  this  population?   c. What  is  the  median  change  score?   d. Find  the  change  score  that  is  2.2  standard  deviations  below  the  mean.     EXERCISE  9   Three  students  were  applying  to  the  same  graduate  school.    They  came  from  schools  with   different  grading  systems.    Which  student  had  the  best  G.P.A.  when  compared  to  his  school?     Explain  how  you  determined  your  answer.             EXERCISE  10   Given  the  following  box  plot:               a. Which  quarter  has  the  smallest  spread  of  data?    What  is  that  spread?   b. Which  quarter  has  the  largest  spread  of  data?  What  is  that  spread?   Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 6 of 20 c. Find  the  Inter  Quartile  Range  (IQR).   d. Are  there  more  data  in  the  interval  5  -­‐  10  or  in  the  interval  10  -­‐  13?    How  do  you  know   this?   e. Which  interval  has  the  fewest  data  in  it?    How  do  you  know  this?   i. 0-­‐2   ii. 2-­‐4   iii. 10-­‐12   iv. 12-­‐13         EXERCISE  11   Given  the  following  box  plot:     a. Think  of  an  example  (in  words)  where  the  data  might  fit  into  the  above  box  plot.    In  2-­‐5   sentences,  write  down  the  example.   b. What  does  it  mean  to  have  the  first  and  second  quartiles  so  close  together,  while  the   second  to  fourth  quartiles  are  far  apart?         EXERCISE  12   Santa  Clara  County,  CA,  has  approximately  27,873  Japanese-­‐Americans.    Their  ages  are  as   follows.    (Source:    West  magazine)   a. Construct  a  histogram  of  the  Japanese-­‐American  community  in  Santa  Clara  What   percent  of  the  community  is  under  age  35?   b. Which  box  plot  most  resembles  the  information  above?     Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 7 of 20       EXERCISE  13     Suppose  that  three  book  publishers  were  interested  in  the  number  of  fiction  paperbacks  adult  consumers   purchase  per  month.    Each  publisher  conducted  a  survey.    In  the  survey,  each  asked  adult  consumers  the   number  of  fiction  paperbacks  they  had  purchased  the  previous  month.    The  results  are  below.           a. Find  the  relative  frequencies  for  each  survey.    Write  them  in  the  charts.     b. Using  either  a  graphing  calculator,  computer,  or  by  hand,  use  the  frequency  column   to  construct  a  histogram  for  each  publisher's  survey.    For  Publishers  A  and  B,  make   bar  widths  of  1.  For  Publisher  C,  make  bar  widths  of  2.   Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 10 of 20   a. The medians for all three graphs are the same. b. We cannot determine if any of the means for the three graphs is different. c. The standard deviation for (b) is larger than the standard deviation for (a). d. We cannot determine if any of the third quartiles for the three graphs is different. EXERCISE  16   Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 11 of 20 Refer  to  the  following  box  plots.         a. In  complete  sentences,  explain  why  each  statement  is  false.   i. Data  1  has  more  data  values  above  2  than  Data  2  has  above  2.   ii. The  data  sets  cannot  have  the  same  mode.   iii. For  Data  1,  there  are  more  data  values  below  4  than  there  are  above  4.   b. For  which  group,  Data  1  or  Data  2,  is  the  value  of  “7”  more  likely  to  be  an  outlier?     Explain  why  in  complete  sentences                                 EXERCISE  17   In  a  recent  issue  of  the  IEEE  Spectrum,  84  engineering  conferences  were  announced.  Four   conferences  lasted  two  days.  Thirty-­‐six  lasted  three  days.  Eighteen  lasted  four  days.  Nineteen   lasted  five  days.  Four  lasted  six  days.  One  lasted  seven  days.  One  lasted  eight  days.  One  lasted   nine  days.  Let  X  =  the  length  (in  days)  of  an  engineering  conference.   Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 12 of 20 a. Organize  the  data  in  a  chart.   b. Find  the  median,  the  first  quartile,  and  the  third  quartile.   c. Find  the  65th  percentile.   d. Find  the  10th  percentile.   e. Construct  a  box  plot  of  the  data.   f. The  middle  50%  of  the  conferences  last  from  _____  days  to  _____  days.   g. Calculate  the  sample  mean  of  days  of  engineering  conferences.   h. Calculate  the  sample  standard  deviation  of  days  of  engineering  conferences.   i. Find  the  mode.   j. If  you  were  planning  an  engineering  conference,  which  would  you  choose  as  the   length  of  the  conference:  mean;  median;  or  mode?  Explain  why  you  made  that   choice.   k. Give  two  reasons  why  you  think  that  3  -­‐  5  days  seem  to  be  popular  lengths  of   engineering  conferences.   EXERCISE  18   A  survey  of  enrollment  at  35  community  colleges  across  the  United  States  yielded  the  following   figures  (source:  Microsoft  Bookshelf):   6414;    1550;    2109;    9350;    21828;    4300;    5944;    5722;    2825;    2044;    5481;    5200;    5853;    2750;     10012;    6357;    27000;    9414;    7681;    3200;    17500;    9200;    7380;    18314;    6557;    13713;    17768;     7493;    2771;    2861;    1263;    7285;    28165;    5080;    11622   a. Organize  the  data  into  a  chart  with  five  intervals  of  equal  width.  Label  the  two   columns  "Enrollment"  and  "Frequency."   b. Construct  a  histogram  of  the  data.   c. If  you  were  to  build  a  new  community  college,  which  piece  of  information  would  be   more  valuable:  the  mode  or  the  average  size?   d. Calculate  the  sample  average.   e. Calculate  the  sample  standard  deviation.   f. A  school  with  an  enrollment  of  8000  would  be  how  many  standard  deviations  away   from  the  mean?     EXERCISE  19   The  median  age  of  the  U.S.  population  in  1980  was  30.0  years.    In  1991,  the  median  age  was   33.1  years.    (Source:    Bureau  of  the  Census)   Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 15 of 20   EXERCISE  23   Student  grades  on  a  chemistry  exam  were:       {  77,  78,  76,  81,  86,  51,  79,  82,  84,  99}   a. Construct  a  stem-­‐and-­‐leaf  plot  of  the  data.   b. Are  there  any  potential  outliers?    If  so,  which  scores  are  they?    Why  do  you  consider   them  outliers?   Try  these  multiple  choice  questions  (Exercises  24  –  30).   The  next  three  questions  refer  to  the  following  information.    We  are  interested  in  the  number  of   years  students  in  a  particular  elementary  statistics  class  have  lived  in  California.                   Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 16 of 20   EXERCISE  24   What  is  the  IQR?   a. 8   b. 11   c. 15   d. 35         EXERCISE  25   What  is  the  mode?   a. 19   b. 19.5   c. 14  and  20   d. 22.65   EXERCISE  26   Is  this  a  sample  or  the  entire  population?   a. Sample   b. Entire  population   c. Neither   The  next  two  questions  refer  to  the  following  table.  X  =  the  number  of  days  per  week  that  100   clients  use  a  particular  exercise  facility.   Source URL: http://cnx.org/content/m16801/latest/ Saylor URL: http://saylor.org/courses/bus204 Attributed to: [Susan Dean and Barbara Illowksy] Saylor.org Page 17 of 20   EXERCISE  27   The  80th  percentile  is:   a. 5   b. 80   c. 3   d. 4   EXERCISE  28   The  number  that  is  1.5  standard  deviations  BELOW  the  mean  is  approximately:       a. 0.7   b. 4.8   c. -­‐2.8   d. Cannot  be  determined   The  next  two  questions  refer  to  the  following  histogram.    Suppose  one  hundred  eleven  people   who  shopped  in  a  special  T-­‐shirt  store  were  asked  the  number  of  T-­‐shirts  they  own  costing  more   than  $19  each.