5. These data represent the record high temperatures in degrees Fahrenheit (F) for each of the 50 states.

Construct a frequency distribution using a class width of 5 degrees, beginning with a lower class limit of 100. Include a column for relative frequency and cumulative frequency.

Also, make a relative frequency histogram.

Data: 112, 100, 127, 120, 134, 118, 105, 110, 109, 112, 110, 118, 117, 116, 118, 122, 114, 114, 105, 109, 107, 112, 114, 115, 118, 117, 118, 122, 106, 110, 116, 108, 110, 121, 113, 120, 119, 111, 104, 111, 120, 113, 120, 117, 105, 110, 118, 112, 114, 114

When creating a frequency distribution, start by dividing the data into classes. Determine the frequency, relative frequency, and cumulative frequency of each class. Finally, construct a histogram using the relative frequencies and classes.

Explanation:

To construct a frequency distribution with a class width of 5 degrees, starting at 100, first divide the data into classes. Since the highest temperature is 134 degrees, the classes would be 100-104, 105-109, 110-114, 115-119, 120-124, 125-129, and 130-134. Next, count the frequency of each class, i.e., how many temperatures fall into each class.

The relative frequency of each class is the frequency divided by the total number of data points, which in this case is 50. Multiply the result by 100 to convert it into a percentage. The cumulative frequency is obtained by adding up the frequencies as you move down the classes.

To create a histogram, plot the relative frequency on the y-axis and the classes on the x-axis. Each class is represented by a bar and the height is proportional to its relative frequency.

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