The Survey of Earned Doctorates regularly assesses the numbers and types of doctorates awarded at U.S. universities.It also provides data on the length of time, in years, it takes to complete a doctorate. Below is a modified list of this completion-time data, truncated to whole numbers (e.g., 8.7 became simply 8) and shortened to make your analysis easier. These data have been collected every five years since 1982.
8 8 8 8 8 7 6 7 7 7 7 7
6 6 6 6 6 6 7 8 8 8 8 7
6 6 7 7 7 6 11 13 15 15
14 12 9 10 10 9 9 9
a. Create a frequency table for these data.
b. How many schools have an average completion time of 8 years or less?
c. Is a grouped frequency table necessary? Why or
why not?
d. Describe how these data are distributed
It would be greatly appreciated if you helped
Don't know the answer
Nolan, Susan, Heinz, Thomas. Essentials of Statistics for the Behavioral Sciences, 2nd Edition. Worth Publishers, 2014. VitalBook file.
a. To create a frequency table, we need to count the number of occurrences of each value in the given data set.
First, let's list all the unique values present in the data set:
6, 7, 8, 11, 12, 13, 14, 15
Next, we will count how many times each value appears:
6 appears 8 times
7 appears 12 times
8 appears 8 times
11 appears 1 time
12 appears 1 time
13 appears 1 time
14 appears 1 time
15 appears 2 times
The frequency table for these data is as follows:
Completion Time (in years) | Frequency
--------------------------------------
6 | 8
7 | 12
8 | 8
11 | 1
12 | 1
13 | 1
14 | 1
15 | 2
b. To determine how many schools have an average completion time of 8 years or less, we need to sum up the frequencies of completion times 8 and below.
Summing the frequencies for completion times 8 and below:
Frequency for 6: 8
Frequency for 7: 12
Frequency for 8: 8
Total: 8 + 12 + 8 = 28
Therefore, there are 28 schools with an average completion time of 8 years or less.
c. A grouped frequency table is not necessary for this data set because the values are already given individually and aren't too numerous. Grouping is typically used when dealing with larger data sets that have a wide range of values in order to simplify the representation.
d. To describe how these data are distributed, we can observe that the majority of completion times fall within the range of 6 to 8 years, with a few occurrences at 11, 12, 13, 14, and 15 years. The distribution is skewed to the right (positively skewed) since the most frequent completion times are on the lower end.