Binned Frequency Table

Question

The exam results for unit 1 are given below. Complete the frequency table columns for this data (using 10 point bins)..

(Round the relative frequencies to the nearest tenth.)

75, 75, 88, 91, 78, 95, 83, 85, 70, 93, 76, 80, 86, 69, 78, 85, 86, 72, 73, 92, 89, 78, 68, 79, 84, 90, 65, 87, 83, 89, 86, 75, 83, 80, 80, 90, 94, 95, 78, 78.
 
 
.
  Bin                       Frequency
60-69                         ?

70-79                          ?

80-89                          ?

90-99                           ?
 
 
 
 

Bin                   Relative Frequency
60-69                      ?

70-79                       ?

80-89                      ?

90-99                      ?
 
 
 
 

Bin                    Cumulative Frequency
60-69                       ?

70-79                           ?

80-89                       ?

90-99                       ?

 
 
 

Answer 1

Sorry but there's no non-tedious way to do this problem.  You just have to count up how many scores fit into each bin.  I counted 3 in the 60-69 bin, so that would have a frequency of 3.  The sum of all the frequencies should add up to the total number of data points, which I think is 40.  

 

To calculate the relative frequencies just divide each frequency by the total, for example 3/40 = 0.075 ~ 0.1.  The frequencies should add up to 1 (except for rounding errors).  

 

To find the cumulative frequencies just add up the relative frequencies in order.  For example, if the first 2 relative frequencies were 0.1 and 0.4 then the first 2 cumulative frequencies would be 0.1 and 0.5.  

 

I'm surprised they tell you to round the relative frequencies to the nearest tenth, as this is a big rounding error.  Maybe they want you to enter the relative frequencies as a percentage, so 3/40 would be 7.5%.