Question

Data from the StudentSurvey dataset are given. Construct a relative frequency table of the data using the categories given. Give the relative frequencies rounded to three decimal places. Of the 362 students who answered the question about what award they would prefer, 31 preferred an Academy Award, 149 preferred a Nobel Prize, and 182 preferred an Olympic gold medal. $\mathbf{2} .

Short answer

The relative frequencies for the preferred awards are: Academy Award: 0.086, Nobel Prize: 0.412, Olympic Gold Medal: 0.503.

Step-by-step solution

Calculate the Total Number of Students

To find the relative frequencies, we first need the total number of students which is 362.

Calculate the Relative Frequencies

The relative frequency of a category can be obtained by dividing the number of students in that category by the total number of students. That is, for the Academy Award, the equation will be \( \frac{31}{362} \). For the Nobel Prize, it will be \( \frac{149}{362} \), and for the Olympic gold medal, it would be \( \frac{182}{362} \).

Round the Relative Frequencies

Following the rounding instructions to three decimal places: the Academy Award relative frequency is 0.086, the Nobel Prize is 0.412, and the Olympic gold medal is 0.503.

Construct the Relative Frequency Table

The table should have two columns: 'Category' and 'Relative Frequency'. The 'Category' column will list: 'Academy Award', 'Nobel Prize', and 'Olympic gold medal'. The 'Relative Frequency' column will list the corresponding relative frequencies we calculated: 0.086, 0.412, and 0.503.