Let's address the two parts of this problem based on the images provided.

Part (a) - Completing the Grouped Frequency Distribution:

We are given the following temperature data:

116, 98, 110, 103, 102,
117, 105, 99, 107, 113,
113, 113, 114, 104, 108

The class width is 5, and we need to group the data and calculate the frequency for each temperature range.

We can define the temperature ranges as follows:

• 98 to 102
• 103 to 107
• 108 to 112
• 113 to 117

Now, we count how many temperatures fall into each class:

1. 98 to 102: 98, 99, 102 (3 temperatures)
2. 103 to 107: 103, 105, 104, 107 (4 temperatures)
3. 108 to 112: 110, 113, 113, 113, 108 (5 temperatures)
4. 113 to 117: 116, 117, 113, 114 (4 temperatures)

So the frequency distribution would look like this:

Part (b) - Constructing the Histogram:

A histogram is a graphical representation of the frequency distribution. Each temperature range (class) will be represented by a bar. The height of each bar corresponds to the frequency of temperatures in that range.

For this specific problem, we will create bars for each of the temperature ranges and use the following frequencies:

• 98 to 102: 3
• 103 to 107: 4
• 108 to 112: 5
• 113 to 117: 4

Would you like me to help you create the histogram visually or explain any additional details?

Questions to explore further:

1. How do you determine the appropriate class width for a frequency distribution?
2. Why is it important to have a consistent class width when constructing a histogram?
3. How does changing the class width affect the shape of the histogram?
4. What are the advantages of grouping data in this way (using frequency distributions)?
5. How does the histogram help in interpreting the distribution of the data?

Tip:

When constructing histograms, always ensure the bars do not overlap and that the width of each bar corresponds to the class width.