Use 8-point bins (92 to 99, to 84 to 91, etc.) to make a frequency table for the data set below. Include columns for relative frequency and cumulative frequency. 73 84 96 80 72 91 77 96 75 81 97 85 84 73 90 75 83 79 75 80
To create a frequency table using 8-point bins for the given data set, follow these steps:
Step 1: Sort the data in ascending order.
72, 73, 73, 75, 75, 75, 77, 79, 80, 80, 81, 83, 84, 84, 85, 90, 91, 96, 96, 97
Step 2: Determine the range of the data set. The range is the difference between the maximum and minimum values.
Range = 97 - 72 = 25
Step 3: Divide the range by the desired bin size (8) to determine the number of bins.
Number of bins = Range/bin size = 25/8 = 3.125
Since the number of bins should be a whole number, round up to the nearest integer.
Number of bins = 4
Step 4: Determine the width of each bin.
Width of each bin = Range/Number of bins = 25/4 = 6.25
Round the bin width to a suitable value, such as 6 or 7.
Width of each bin = 6
Now, let's create the frequency table:
Bin | Frequency | Relative Frequency | Cumulative Frequency
------------------------------------------------------------------------
72 to 77 | 6 | 6/20 = 0.3 | 6
78 to 83 | 4 | 4/20 = 0.2 | 10
84 to 89 | 2 | 2/20 = 0.1 | 12
90 to 95 | 3 | 3/20 = 0.15 | 15
96 to 101 | 5 | 5/20 = 0.25 | 20
Explanation:
To create the frequency table, we divide the data into bins based on the specified bin size. The lower limit of the first bin is 72, and the width of each bin is 6. Starting from the first bin, we count the number of data points that fall within each bin range.
For example, in the first bin (72 to 77), there are 6 data points: 72, 73, 73, 75, 75, and 75. These 6 data points have a frequency of 6.
To calculate the relative frequency, we divide the frequency in each bin by the total number of data points. The total number of data points is 20 in this case. For the first bin, the relative frequency is 6/20, which simplifies to 0.3.
The cumulative frequency represents the running total of frequencies. To calculate the cumulative frequency for each bin, we add the frequency of the bin to the cumulative frequency of the previous bin. The cumulative frequency of the first bin is simply its frequency, which is 6. For the second bin, we add its frequency (4) to the cumulative frequency of the first bin (6), resulting in a cumulative frequency of 10.
Repeat this process for each bin until you have the desired frequency table.