Question

An instructor asks students to rate their anxiety level on a scale of 1 to 100 (1 being low anxiety and 100 being high anxiety) just before the students take their final exam. The responses are shown below. Construct a relative frequency table for the instructor using five classes. Use the minimum value from the data set as the lower class limit for the first row, and use the lowest possible whole-number class width that will allow the table to account for all of the responses. Use integers or decimals for all answers.
48,50,71,58,56,55,53,70,63,74,64,33,34,39,49,60,65,84,54,58
Provide your answer below:
Lower Class Limit Upper Class Limit Relative Frequency

Answer 1

Answer:

The frequency table is shown below.

Step-by-step explanation:

The data set arranged ascending order is:

S = {33 , 34 , 39 , 48 , 49 , 50 , 53 , 54 , 55 , 56 , 58 , 58,  60 , 63 , 64 , 65 , 70 , 71 , 74 , 84}

It is asked to use the minimum value from the data set as the lower class limit for the first row.

So, the lower class limit for the first class interval is 33.

To determine the class width compute the range as follows:

$\text{Range}=\text{Maximum}-\text{Minimum}$

          $=84-33\\=51$

The number of classes requires is 5.

The class width is:

$\text{Class width}=\frac{Range}{5}=\frac{51}{2}=10.2\approx 10$

So, the class width is 10.

The classes are:

33 - 42

43 - 52

53 - 62

63 - 72

73 - 82

83 - 92

Compute the frequencies of each class as follows:

Class Interval                  Values                        Frequency

   33 - 42                      33 , 34 , 39                             3

   43 - 52                      48 , 49 , 50                            3

   53 - 62          53 , 54 , 55 , 56 , 58 , 58,  60              7

   63 - 72                 63 , 64 , 65 , 70 , 71                      5

   73 - 82                              74                                  1

   83 - 92                             84                                   1

   TOTAL                                                                   20

Compute the relative frequencies as follows:

Class Interval          Frequency        Relative Frequency

   33 - 42                        3                   $\frac{3}{20}\times 100\%=15\%$

   43 - 52                        3                   $\frac{3}{20}\times 100\%=15\%$

   53 - 62                        7                   $\frac{7}{20}\times 100\%=35\%$

   63 - 72                        5                   $\frac{5}{20}\times 100\%=25\%$

   73 - 82                         1                   $\frac{1}{20}\times 100\%=5\%$

   83 - 92                         1                   $\frac{1}{20}\times 100\%=5\%$

   TOTAL                        20                          100%