Exercises

1. A group of students was surveyed and asked the following question: "How many hours do you typically spend playing video games each week?". Each student was instructed to select one of five choices and the results of the survey are shown in the graph below.
   
   1. How many students were surveyed in total?
   2. Did more or less than half of the students give an answer of \(8\) hours or more?
   3. Can you determine what particular number of hours was the most common for this group of students? Explain.
2. The following frequency graph records the length of each of the first \(100\) words in a certain book.
   
   1. Explain how you can obtain a relative frequency graph from the given graph.
   2. What percentage of the words have length greater than \(5\)?
   3. Find three word lengths that combine to represent exactly half of the recorded values.
3. Products can be classified as either grade A, B, C, D or E, where grade A represents the highest quality and grade E represents the lowest quality. A single company collected \(20\) products and the quality of each product was recorded as follows:
   E
   E

   D
   C

   C
   D

   C
   A

   B
   A

   A
   B

   C
   C

   D
   C

   E
   C

   E
   B
   Complete the table below using the data given above and then create a frequency graph and a relative frequency graph of the data.

   Grade	Tally	Frequency	Relative Frequency
   A
   B
   C
   D
   E

4. The following graphs summarize the ratings of two different restaurants recorded during two separate surveys.

   Restaurant 1 Ratings
   

   Restaurant 2 Ratings
   

   For each survey, determine whether ratings of \(3\) or less represent approximately one quarter of the total responses. Did you find it easier to determine the answer for Restaurant 1 or Restaurant 2? 

5. A teacher recorded the contest scores of \(50\) students to see how well students in the school performed on the Gauss math contest. The scores are shown below.
   \(92\)
   \(60\)
   \(76\)
   \(78\)
   \(55\)

   \(96\)
   \(79\)
   \(84\)
   \(107\)
   \(62\)

   \(105\)
   \(40\)
   \(58\)
   \(120\)
   \(40\)

   \(96\)
   \(90\)
   \(137\)
   \(97\)
   \(78\)

   \(108\)
   \(138\)
   \(140\)
   \(128\)
   \(129\)

   \(113\)
   \(94\)
   \(105\)
   \(116\)
   \(94\)

   \(106\)
   \(94\)
   \(127\)
   \(105\)
   \(136\)

   \(104\)
   \(80\)
   \(65\)
   \(83\)
   \(94\)

   \(96\)
   \(90\)
   \(68\)
   \(127\)
   \(72\)

   \(140\)
   \(136\)
   \(140\)
   \(105\)
   \(110\)

   The teacher decided that it would be helpful to further organize the data and create a graph to display the scores.

   1. Divide the \(50\) scores into five categories and record the frequencies in the table below. Create a frequency bar graph with the five categories on the horizontal axis.

      Score Category	Frequency
      \(40-59\)
      \(60-79\)
      \(80-99\)
      \(100-119\)
      \(120-140\)

   2. What percentage of students received a score of \(120\) or above on the contest?
6. The temperatures on \(50\) different days during the year were recorded. Many of the entries are missing in the table of recordings below. 

   Temperature			\(0^{\circ}\)C to \(5^{\circ}\)C
   Frequency		\(10\)		\(25\)
   Relative Frequency	\(10\%\)	\(20\%\)

   Complete the table by filling in the missing entries appropriately. Are there any entries for which you have different possibilities?
7. A class of \(30\) students attended a movie. Each student attended the movie with one parent. A survey was conducted as the parents and students exited a movie theatre. The surveyor was hoping to determine whether or not parents and their children enjoyed the movie. The results of the survey are shown in the graphs below.
   Ratings by Parents
   

   Ratings by Children
   What information can you find by looking at each graph individually? What information can you find by comparing the two graphs?
8. When the telephone network system used to be electromechanical, rather than digital as it is today, wrong connections were much more likely to occur. During a study of wrong connections, observations were recorded for \(267\) distinct telephone numbers. The data is recorded in the table below:

   Number of Wrong Connections	\(2\) or less	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)	\(13\)	\(14\)	\(15\)	\(16\) or more
   Number of Telephone Numbers	\(1\)	\(5\)	\(11\)	\(14\)	\(22\)	\(43\)	\(31\)	\(40\)	\(35\)	\(20\)	\(18\)	\(12\)	\(7\)	\(6\)	\(2\)

   1. What percentage of the \(267\) telephone numbers experienced \(13\) or more wrong connections?
   2. Find the smallest value of \(n\) for which at least \(75\%\) of the \(267\) phone numbers experienced \(n\) or more wrong connections.
   3. Assume that the single telephone number in the column "\(2\) or less" experienced exactly \(2\) wrong connections, and that the \(2\) telephone numbers in the column "\(16\) or more" both experienced \(16\) wrong connections. Can you calculate the average (mean) number of wrong connections experienced by these \(267\) telephone numbers?
   4. If you do not assume the extra information from part c), explain why you cannot calculate the average number of wrong connections from the data in the table. Can you determine the smallest possible average? Can you determine the largest possible average?