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The state gas tax in cents per gallon for 25 states is given below:

118.2, 114.6, 113.1, 111.9, 110.0, 108.8, 108.3, 107.7, 107.0, 106.7, 105.3, 103.7, 103.2, 102.8, 101.6, 99.8, 98.1, 96.6, 95.7, 93.6, 92.5, 91.0, 90.0, 87.1, 83.1

a) Construct its grouped frequency distribution by the Sturges rule. [5]

b) From 6 a) above, construct its "less than" and "more than" cumulative frequency distributions. [6]

c) Construct the histogram and the cumulative frequency polygon of the data from 6 a) above. [6]

Answer :

Final answer:

The question is about constructing grouped frequency and cumulative frequency distributions, and then using these distributions to create a histogram and a cumulative frequency polygon. This involves utilizing a mathematical approach including Sturges' rule, calculations of class intervals, and understanding of how to graphically represent statistical data.

Explanation:

To answer the question, we'll need to use grouped frequency distribution, cumulative frequency distribution, and create a histogram and cumulative frequency polygon.

  1. Grouped Frequency Distribution: Following the Sturges' rule, the number of groups (k) is calculated by the formula k = 1 + 3.322(log N), where N is the number of observations. Then, we calculate the range of the data which is Max-Min and divide it by the number of groups. This will give us class intervals. Now, we check how many observations fall into each group to get the frequency.
  2. Cumulative Frequency Distributions: The 'less than' cumulative frequency is found by progressively adding the frequencies. For the 'more than' cumulative frequency, start with the total number of observations and subtract the frequency of the first group, then subtract the frequency of the second group and so on.
  3. Histogram and Cumulative Frequency Polygon: To construct a histogram, put the class intervals on the x-axis and the frequencies on the y-axis. For the cumulative frequency polygon, use the upper limit of each interval on the x-axis and the cumulative frequency for each class on the y-axis. Join the points to form the polygon.

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