Questions: Use 9 point bins (91 to 99, 82 to 90, etc) to make a frequency table for the data set below. Include columns for relative frequency and cumulative frequency:
99, 70, 93, 80, 86, 89, 72, 99, 99, 95,
77, 89, 95, 64, 88, 71, 66, 91, 73, 69
Complete the table.
(Type integers or decimals rounded to the nearest tenth as needed.)
Data Frequency Relative frequency Cumulative frequency
91 to 99
x
Transcript text: Use 9 point bins ( 91 to 99,82 to 90 , etc) to make a frequency table for the data set below. Include columns for relative frequency and cumulative trequency:
\begin{tabular}{llllllllll}
99 & 70 & 93 & 80 & 86 & 89 & 72 & 99 & 99 & 95 \\
77 & 89 & 95 & 64 & 88 & 71 & 66 & 91 & 73 & 69
\end{tabular}
Complete the table.
(Type integers or decimals rounded to the nearest tenth as needed.)
Data Frequency Relative frequency Cumulative frequency
91 to 99 $\square$
$\square$ x
Solution
Solution Steps
Step 1: Determine Bin Boundaries
Given a bin range of 9, the bin boundaries are calculated based on the data set's minimum and maximum values.
Bin Boundaries: [64, 73, 82, 91, 100]
Step 2: Sort Data
The data set is sorted in ascending order to facilitate the tallying of frequencies.
Sorted Data: [64, 66, 69, 70, 71, 72, 73, 77, 80, 86, 88, 89, 89, 91, 93, 95, 95, 99, 99, 99]
Step 3: Tally Frequencies
For each data point, the corresponding bin's frequency count is incremented.
Bin 64 to 73: 6
Bin 73 to 82: 3
Bin 82 to 91: 4
Bin 91 to 100: 7
Step 4: Calculate Relative Frequencies
Each bin's frequency is divided by the total number of data points to find the relative frequency.
Bin 64 to 73: 0.3
Bin 73 to 82: 0.1
Bin 82 to 91: 0.2
Bin 91 to 100: 0.3
Step 5: Calculate Cumulative Frequencies
The cumulative frequency of each bin is calculated by adding its frequency to the cumulative frequency of all previous bins.
Bin 64 to 73: 6
Bin 73 to 82: 9
Bin 82 to 91: 13
Bin 91 to 100: 20
Final Answer:
| Bin Range | Frequency | Relative Frequency | Cumulative Frequency |
|-|-|+|+|
| 64 to 73 | 6 | 0.3 | 6 |
| 73 to 82 | 3 | 0.1 | 9 |
| 82 to 91 | 4 | 0.2 | 13 |
| 91 to 100 | 7 | 0.3 | 20 |