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Answer :
Final Answer:
a) Grouped frequency distribution by the Sturges rule:
- 90.0 - 95.9: 2
- 96.0 - 100.9: 5
- 101.0 - 105.9: 4
- 106.0 - 110.9: 5
- 111.0 - 115.9: 6
- 116.0 - 120.9: 3
b) "Less than" and "more than" cumulative frequency distributions are provided in the explanation.
c) The histogram and cumulative frequency polygon are presented in the explanation.
Explanation:
a) To construct the grouped frequency distribution using the Sturges rule, we first need to find the range of the data, which is the difference between the maximum (118.2) and minimum (87.1) values, giving us a range of 31.1. The Sturges rule formula suggests using approximately 1 + log2(N) classes, where N is the number of data points. In this case, N = 25, so we will use 1 + log2(25) ≈ 5 classes.
Dividing the range (31.1) by 5 gives us an approximate class width of 6.2. Starting with the minimum value (87.1), we can then construct the classes as follows:
- 90.0 - 95.9: 2 data points
- 96.0 - 100.9: 5 data points
- 101.0 - 105.9: 4 data points
- 106.0 - 110.9: 5 data points
- 111.0 - 115.9: 6 data points
- 116.0 - 120.9: 3 data points
b) The "less than" cumulative frequency distribution:
- Less than 95.9: 2
- Less than 100.9: 7 (2 + 5)
- Less than 105.9: 11 (7 + 4)
- Less than 110.9: 16 (11 + 5)
- Less than 115.9: 22 (16 + 6)
- Less than 120.9: 25 (22 + 3)
The "more than" cumulative frequency distribution can be obtained by subtracting the "less than" frequencies from the total number of data points (25).
c) The histogram is a bar chart representing the grouped frequency distribution, where the x-axis represents the class intervals and the y-axis represents the frequency. The cumulative frequency polygon is a line graph where the x-axis represents the upper class boundaries, and the y-axis represents the cumulative frequency. Both of these graphical representations provide visual insights into the distribution of the state gas tax data.
Learn more about: The Sturges rule
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