Question

Question 1 :

Recent data from North America’s largest cities provide insight into the amount of time residents spend waiting in traffic during the course of a single year. Following is the number of hours residents in 31 cities waited in traffic per year.

47      54      42      74      38      33      20      45      27      71

30      35      23      43      35      21      20      45      57      49

25      35      27      28      19      44      37      50      37      64      38

Use this data set to compute the following descriptive statistics:

a. Mean   ________       b. Median _________          c. Mode __________     

d. Range ________       e. Variance ________        f. Standard Deviation ________      

g. Which one of these descriptive statistics is not measured in the same units as the data?

___________________________________________

h. Compute the Coefficient of Variation ___________

i. State the first quartile and explain its meaning. _______________________________

j. State the third quartile and explain its meaning. _______________________________

k. List the Five-number summary: ______________________________________________

l. Are the data skewed? If so, how? ____________________________________________

m. Does the data set contain any outliers? Explain. _________________________________

Answer 1

• Mean
  The mean is given by:
  
  
• Median
  The median is the middle most value of the ordered data.
  That is, observation of the ordered data.
  
  The ordered data is given by:

  19
  20
  20
  21
  23
  25
  27
  27
  28
  30
  33
  35
  35
  35
  37
  37
  38
  38
  42
  43
  44
  45
  45
  47
  49
  50
  54
  57
  64
  71
  74

  
  The observation is 37.
  
  
• Mode
  The mode is the value with the highest frequency.
  We observe that 35 has occured the highest number of times - 3.
  Hence, Mode is 35.
  
  
• Range
  The Min value is 19.
  The Max value is 74.
  
  The Range is 74-19 = 55.
  
  
• Variance
  The variance is calculated as:
  
  
  
• Standard Deviation
  The standard deviation is calculated as:
  
  
  
  
  
• Variance takes squared values. Hence, it is not measured in the same units as the data.
  
  
  
• Coefficient of Variation
  The coefficient of variation is calculated as:
  
  
  
  
  
• First Quartile
  The First Quartile is given by   observation of the ordered data.
  The observation is 27.
  The First Quartile is the value below which 25% of the data lie.
  
• Second Quartile
  The Second Quartile is given by   observation of the ordered data.
  The observation is 47.
  The Second Quartile is the value above which 25% of the data lie.
  
  
• Five Numbered Summary
  The 5 numbered summary is listed below:

  Minimum	19
  First Quartile	27
  Median	37
  Third Quartile	47
  Maximum	74

  
  
  

• It is observed that,
  
  This is the case of Symmetricness.
  Hence, the data is not skewed.
  
  

• Outliers
  It is known that,
  
  It is known that if observations lie below
  or, above
  
  
  It is observed that no such observations exists, and hence has no outliers.
  
  

I hope this clarifies your doubt. If you're satisfied with the solution, hit the Like button. For further clarification, comment below. Thank You. :)