Question

here are the hottest recorded temperatures (in \\(^{\circ}\text{f}\\)) for each of sixteen cities throughout north america.

temperatures (in \\(^{\circ}\text{f}\\))
111, 95, 103, 108, 107, 101, 98, 100
94, 106, 112, 93, 103, 102, 97, 108

(a) complete the grouped frequency distribution for the data. (note that the class width is 4.)

temperatures (in \\(^{\circ}\text{f}\\)) | frequency
93 to 96 |
97 to 100 |
101 to 104 |

(b) construct a histogram for the data.

Explanation:

Sort and tally the temperature data

The 16 temperature values are:
111, 95, 103, 108, 107, 101, 98, 100, 94, 106, 112, 93, 103, 102, 97, 108.

Sorting the data in ascending order:
93, 94, 95, 97, 98, 100, 101, 102, 103, 103, 106, 107, 108, 108, 111, 112.

Calculate frequencies for each class

Using a class width of 4:

• 93 to 96: 93, 94, 95 (3 values)
• 97 to 100: 97, 98, 100 (3 values)
• 101 to 104: 101, 102, 103, 103 (4 values)
• 105 to 108: 106, 107, 108, 108 (4 values)
• 109 to 112: 111, 112 (2 values)

Determine histogram boundaries

The classes and their corresponding frequencies are:

• 93 to 96: 3
• 97 to 100: 3
• 101 to 104: 4
• 105 to 108: 4
• 109 to 112: 2

Answer:

Question (a)

Temperatures (in \(^\circ\text{F}\))	Frequency
97 to 100	3
101 to 104	4
105 to 108	4
109 to 112	2

Question (b)

The histogram is constructed with the following bar heights corresponding to each temperature interval:

• 93 to 96: height of 3
• 97 to 100: height of 3
• 101 to 104: height of 4
• 105 to 108: height of 4
• 109 to 112: height of 2