Sure, let's go through the steps to construct a frequency distribution for the dormancy periods.
1. Understand the data and the specifications:
- We have a dataset of dormancy periods given as: 93, 71, 92, 90, 96, 91, 66, 97, 91, 93, 82, 99, 116, 83, 59, 61, 66, 59, 99, 93, 96, 90, 88, 82, 82, 93, 61, 105, 91, 91.
- We need to construct a frequency distribution table with a class width of 5, starting with the lower class limit of 55.
2. Determine the range of classes:
- The minimum value in the dataset is 59, and the maximum value is 116.
- The classes will begin from 55 and increase in increments of 5.
3. Calculate the number of classes:
- Using the classes defined by our specified width and limits, we calculate the classes as follows:
1. 55-59
2. 60-64
3. 65-69
4. 70-74
5. 75-79
6. 80-84
7. 85-89
8. 90-94
9. 95-99
10. 100-104
11. 105-109
12. 110-114
13. 115-119
4. Construct the frequency distribution:
- Now, we count the number of data points falling into each of the class intervals. Here's the breakdown:
- 55-59: 2 occurrences (59, 59)
- 60-64: 2 occurrences (61, 61)
- 65-69: 2 occurrences (66, 66)
- 70-74: 1 occurrence (71)
- 75-79: 0 occurrences
- 80-84: 4 occurrences (82, 83, 82, 82)
- 85-89: 1 occurrence (88)
- 90-94: 11 occurrences (93, 92, 90, 91, 91, 93, 93, 93, 90, 91, 91)
- 95-99: 5 occurrences (96, 97, 99, 96, 99)
- 100-104: 0 occurrences
- 105-109: 1 occurrence (105)
- 110-114: 0 occurrences
- 115-119: 1 occurrence (116)
Here is the resulting frequency distribution table:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Dormancy Period (min)} & \text{Frequency} \\
\hline 55-59 & 2 \\
\hline 60-64 & 2 \\
\hline 65-69 & 2 \\
\hline 70-74 & 1 \\
\hline 75-79 & 0 \\
\hline 80-84 & 4 \\
\hline 85-89 & 1 \\
\hline 90-94 & 11 \\
\hline 95-99 & 5 \\
\hline 100-104 & 0 \\
\hline 105-109 & 1 \\
\hline 110-114 & 0 \\
\hline 115-119 & 1 \\
\hline
\end{array}
\][/tex]
This table summarizes the frequency of dormancy periods falling within each specified interval.
