Exercise Module Performance Task Page 300

Let's look at the given table about what students would most like to do during their summer vacation.

We are asked to do four things.

1. Make a table showing the relative frequency of each of the six categories in the table.
2. Make a circle graph, histogram, or bar graph showing the frequencies or relative frequencies of each of the six categories in the table.
3. Write and answer at least five questions involving conditional relative probability that can be answered by referring to the table.
4. Describe any trends we see in the data.

   Let's conquer these tasks one step at a time.

   Relative Frequency Table

   We will construct our relative frequency table using percents. To do so, we need to divide each frequency by the grand total and then multiply them by 100. First, to find the grand total, we have to add all the numbers in the table. Grand total: 25+40+15+70+20+30= 200 Now we can divide each cell by 200.

   	Visit a Foreign Country	Attend Camp	Visit a National Park
   Grades 7-9	25/200* 100	40/200* 100	15/200* 100
   Grades 10-12	70/200* 100	20/200* 100	30/200* 100

   After simplifying these values, we have the completed relative frequency table.

   	Visit a Foreign Country	Attend Camp	Visit a National Park
   Grades 7-9	12.5 %	20 %	7.5 %
   Grades 10-12	35 %	10 %	15 %

   Graph Showing Frequencies

   We have decided to construct a bar chart showing the frequencies. Both a circle graph and a histogram would not have worked as well because it is not as easy to show side-by-side comparisons of the two types of students. We will use the y-axis to represent each frequency and the x-axis to represent the activity.

   

   Questions about Conditional Relative Probability

   Next, we need to write and answer at least five questions involving conditional relative probability that can be answered by referring to the table. Please note that these are only a few examples of questions that could have been asked. There are many more options.

   Question	Answer
   1. Given that a student is in grade 7,8, or 9, what is the probability he/she wants to visit a foreign country?	25 of the 80 students in grades 7-9 want to visit a foreign country. Therefore, the probability that a student wants to visit a foreign country, given that he/she is in year 7,8, or 9, is 2580= 516.
   2. Given that a student wants to visit a foreign country, what is the probability he/she is in grades 10-12?	70 of the 95 students who want to visit a foreign country are in grades 10-12. Therefore, the probability that a student is in grades 10-12, given that he/she wants to visit a foreign country is 7095= 1419.
   3. Given that a student wants to attend a camp, what is the probability he/she is in grades 7-9?	40 of the 60 students who want to attend a camp are in grades 7-9. Therefore, the probability that a student is in grades 7-9, given that he/she wants to attend a camp is 4060= 23.
   4. Given that a student wants to visit a national park, what is the probability he/she is in grades 10-12?	30 of the 45 students who want to visit a national park are in grades 10-12. Therefore, the probability that a student is in grades 10-12, given that he/she wants to visit a national park is 3045= 23.
   5. Given that a student is in grades 10-12, what is the probability he/she wants to visit a national park?	30 of the 120 students in grades 10-12 want to visit a national park. Therefore, the probability that a student wants to visit a national park, given that he/she is in grades 10-12, is 30120= 14.

   Describe Any Trends

   A big part of data analysis is describing trends in the data. For this data, let's use the relative frequency table constructed and the graph drawn.

   • Grades 7-9 represent 40 % of the total and grades 10-12 represent 60 % .
   • If an activity has to be arranged for all the students, visiting a foreign country would be the recommended one, since 47.5 % of the students have chosen it.
   • The least chosen activity in general is visiting a national park, being chosen by 22.5 % of the students.
   • The most chosen activity for grades 7-9 is attending a camp.
   • The most chosen activity for grades 10-12 is visiting a foreign country.