Department of Mathematical Sciences | Kent State University



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|Elementary Probability And Statistics  TEST 1   |

|  | Name:                             Score:                          |

1 . he table below list the students in a statistics class along with their favorite color.

|Name |Favorite Color |

|Brian |Blue |

|Christine |Red |

|Russell |Yellow |

|Mindy |Orange |

|Cassie |Purple |

|Jennifer |Blue |

|Edward |Blue |

|Justin |Blue |

|Jason |Green |

|Jasmina |Purple |

|Dawn |Red |

|Aaron |Green |

|Raquel |Orange |

|Erin |Purple |

|Amber |Red |

|Eric |Blue |

|Stephanie |Green |

|Megan |Orange |

|Edith |Yellow |

What is the relative frequency for the color blue?

|[pic]  |4 |

|[pic]  |26% |

|[pic]  |5 |

|[pic]  |20% |

[pic]2.  Which of the following are used to misrepresent data using bar graphs?

|[pic]  |use a relative frequency bar graph rather than a frequency bar graph |

|[pic]  |start the scale at a value other than zero |

|[pic]  |use a Pareto chart |

|[pic]  |none of the above |

[pic] 3.   Side-by-side bar graphs should be used when [pic]

|[pic]  |the data set is very large |

|[pic]  |constructing frequency bar graphs |

|[pic]  |comparing two data sets |

|[pic]  |the data set is very small |

  

[pic]4.  Use the following sample data, which lists the number of minutes 30 statistics students spend commuting to Joliet Junior College from their homes.

|30 |25 |15 |5 |18 |35 |45 |60 |20 |25 |

|10 |5 |30 |40 |15 |22 |10 |15 |20 |5 |

|45 |35 |10 |24 |18 |15 |30 |20 |21 |18 |

With the first class having a lower limit of 5 and a class with of 5, how may classes would you need for this data set?

a) 10 b) 11 c) 9 d)12

[pic]5 . Refer back to question 4. What is the relative frequency for the 6th class? [pic]

|[pic]  |1/5 |

|[pic]  |1/10 |

|[pic]  |7/30 |

|[pic]  |1/6 |

  

[pic]6 . Refer back to question 4. How would increasing the class width affect the overall shape of the histogram? [pic]

|[pic]  |It would make the histogram more skewed. |

|[pic]  |It would make the histogram more symmetric. |

|[pic]  |It would remain the same. |

|[pic]  |none of the above |

[pic]7.  In creating classes for summarizing continuous data, which of the following should be considered?

|[pic]  |the highest and lowest values in the data set |

|[pic]  |the number of data pieces |

|[pic]  |the number of decimal places for the values in the data set |

|[pic]  |all of the above |

  

[pic]

8.  What is a primary reason for splitting the stems in a stem-and-leaf plot?

|[pic]  |The data are very spread out. |

|[pic]  |There are only a few number of data pieces. |

|[pic]  |There are a large number of data pieces. |

|[pic]  |The data are clumped very closely. |

  

[pic]9 .   An advantage of a stem-and-leaf plot over a histogram is that a stem-and-leaf plot

|[pic]  |is easier to use in determining the distribution shape of the data. |

|[pic]  |shows all of the original raw data. |

|[pic]  |can be constructed in just one way. |

|[pic]  |is less work to create. |

  

[pic]10 .   Histograms differ from bar graphs in that histograms

|[pic]  |can be draw vertically or horizontally. |

|[pic]  |the rectangles/bars are not connected. |

|[pic]  |are used for qualitative data. |

|[pic]  |are used for quantitative data. |

  

[pic]11 .   If a histogram appears to be even on both the left and right side, the shape of its distribution would be best described as which of the following?

a) uniform b) skewed left c) symmetric d) skewed right

 

[pic]12. We can summarize quantitative data by:   

a) histograms b) pie graphs c) stem[pic]-and-leaf plots d) bar graphs

[pic]13 .  If a histogram appears to have many low-valued observations and just a few high-valued observations, the shape of its distribution would be best described as which of the following?

|[pic]  |skewed left |

|[pic]  |skewed right |

|[pic]  |uniform |

|[pic]  |symmetric |

 14 .  What is the class midpoint of the class 11 – 13.99? [pic]

|[pic]  |12.99 |

|[pic]  |2.99 |

|[pic]  |12.495 |

|[pic]  |12.5 |

  

[pic]15 .Which of the following data sets would be best appropriate for using a time series plot?

|[pic]  |age and number of people covered by health insurance |

|[pic]  |magnitude and number of earthquakes |

|[pic]  |time of day and the number of customers in a local grocery store |

|[pic]  |year and the percents of high school graduates enrolled in college |

[pic]16. If graphs unintentionally create an incorrect impression, they can referred to as

a) misleading b) biased c) misrepresented d) deceiving

[pic]17 . Which of the following demonstrates manipulating the vertical scale of a bar graph?

|[pic]  |begin at a value slightly less than the smallest value in the data set rather than at 0 |

|[pic]  |have uneven increments |

|[pic]  |both of the above |

|[pic]  |have unequal spread between the bars |

  

18 . In 1798 the English scientist Henry Cavendish measured the density of the earth with great care. It is common practice to repeat careful measurements several times and use the mean as the final result. Cavendish repeated his work 29 times. Here are the results (the data give the density of the earth as a multiple of the density of water):

|5.50 |5.61 |4.88 |5.07 |5.26 |5.55 |5.36 |5.29 |5.58 |5.65 |

|5.57 |5.53 |5.62 |5.29 |5.44 |5.34 |5.79 |5.10 |5.27 |5.39 |

|5.42 |5.47 |5.63 |5.34 |5.46 |5.30 |5.75 |5.68 |5.85 | |

What is the arithmetic mean, rounded to two decimal places? [pic]

|[pic]  |5.42 |

|[pic]  |5.44 |

|[pic]  |5.45 |

|[pic]  |5.43 |

  

[pic]19.  Refer back to question 18. What is the median?

|[pic][p|5.85 |

|ic]  | |

|[pic]  |5.295 |

|[pic]  |5.46 |

|[pic]  |5.615 |

 

[pic]20 . Refer back to question 18. What is the mode?

|[pic][p|5.29 |

|ic]  | |

|[pic]  |5.34 |

|[pic]  |both of the above |

|[pic]  |There is no mode. |

 

[pic]21 .  Refer back to problems 19 and 20. Based on the values of the mean and the median, the shape of the distribution would be [pic]

|[pic]   |symmetric |

|[pic]   |slightly skewed left |

|[pic]   |slightly skewed right |

|[pic]   |uniform |

22 . Refer back to question 18. What is the range?

|[pic][p|4.88 |

|ic]  | |

|[pic]  |5.85 |

|[pic]  |4.88 to 5.85 |

|[pic]  |0.97 |

[pic]23. Refer back to question 18.. What is the variance to four decimal places?

|[pic][p|0.4690 |

|ic]  | |

|[pic]  |0.2171 |

|[pic]  |0.0484 |

|[pic]  |0.2209 |

[pic]24.  Refer back to question 18.. What is the standard deviation rounded to four decimal places?

|[pic][p|0.2171 |

|ic]  | |

|[pic]  |0.1765 |

|[pic]  |0.3621 |

|[pic]  |0.2209 |

[pic]22 .   Which type of data can the mode be used for?

|[pic][p|discrete |

|ic]  | |

|[pic]  |continuous |

|[pic]  |qualitative |

|[pic]  |all of the above |

[pic]23 .  Which type of data can the arithmetic mean and the median be used for?

|[pic][p|continuous |

|ic]  | |

|[pic]  |discrete |

|[pic]  |both of the above |

|[pic]  |qualitative |

  

[pic]24. The symbol used to denote the arithmetic mean of a population is

a)[pic] b) M c) [pic] d) [pic]

[pic]

 

[pic]27.  The symbol used to denote the standard deviation of a population is

a) S b) [pic] c) s d) M

[pic]28. The distribution of heights of adult men is approximately normal with mean 69 inches and standard deviation 2.5 inches. Using the Empirical Rule, what percentage of adult men have heights between 64 and 74 inches?

a)95 b)99.7 c)68 d)75

[pic]29. Refer back to question 18.. What are the first quartile and the third quartile?

[pic]30. Refer back to question 18.. What is the Five-Number-Summary of the data set?

Bonus Problem:

Refer back to question 18. (10 points)

1) Check the data set, following the steps to check outliers(you must give all steps), can you find any outlier or extreme values? If you can, what’s the value of the observation?

2) Construct a box-plot for the data in question 18.

 

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