Question

here are the hottest recorded temperatures (in °f) for each of sixteen cities throughout north america.
temperatures
(in °f)
94 101 94 110 110 104 108 93
99 109 108 107 103 105 112 102
(a) complete the grouped frequency distribution for the data. (note that the class width is 4.)
temperatures (in °f) frequency
93 to 96
97 to 100
101 to 104
105 to 108
109 to 112
(b) construct a histogram for the data.

Explanation:

Step1: Count 93 - 96

Temperatures: 94, 94, 93, 99? Wait, no. Wait the data is 94, 101, 94, 110, 110, 104, 108, 93, 99, 109, 108, 107, 103, 105, 112, 102. Wait, let's list all 16? Wait the first row: 94, 101, 94, 110, 110, 104, 108, 93 (8 numbers). Second row: 99, 109, 108, 107, 103, 105, 112, 102 (8 numbers). Total 16. Now for 93 - 96: numbers between 93 (inclusive) and 96 (inclusive). So 93, 94, 94. Wait 93, 94, 94. Is 95 there? No. So 93, 94, 94: three numbers? Wait 93, 94, 94, and is 96? No. Wait 93, 94, 94, and 95? No. Wait the numbers: 93, 94, 94. Wait 93 is 93, 94, 94. Then 99 is in 97 - 100. Wait 93 - 96: 93, 94, 94, and is 95? No. Wait 93, 94, 94: that's three? Wait no, 93, 94, 94: three? Wait 93 is one, 94 is two, so total three? Wait 93, 94, 94: 3 numbers.

Step2: 97 - 100: numbers between 97 (inclusive) and 100 (inclusive). So 99. Only 99. So frequency 1.

Step3: 101 - 104: numbers between 101 (inclusive) and 104 (inclusive). So 101, 104, 103, 102. Let's check: 101, 104, 103, 102. So 101, 102, 103, 104. That's four numbers.

Step4: 105 - 108: numbers between 105 (inclusive) and 108 (inclusive). So 108, 108, 107, 105. Let's check: 105, 107, 108, 108. That's four numbers.

Step5: 109 - 112: numbers between 109 (inclusive) and 112 (inclusive). So 110, 110, 109, 112. Let's check: 109, 110, 110, 112. That's four numbers? Wait 109, 110, 110, 112: four? Wait 109, 110, 110, 112: yes. Wait let's count again:

Data list: 94, 101, 94, 110, 110, 104, 108, 93, 99, 109, 108, 107, 103, 105, 112, 102.

Now categorize:

93 - 96: 93, 94, 94 → 3

97 - 100: 99 → 1

101 - 104: 101, 102, 103, 104 → 4

105 - 108: 105, 107, 108, 108 → 4

109 - 112: 109, 110, 110, 112 → 4

Wait but total should be 16. Let's check: 3 + 1 + 4 + 4 + 4 = 16. Yes.

So:

93 to 96: 3

97 to 100: 1

101 to 104: 4

105 to 108: 4

109 to 112: 4

Answer:

For part (a), the grouped frequency distribution is:

Temperatures (in °F)	Frequency
97 to 100	1
101 to 104	4
105 to 108	4
109 to 112	4

For part (b), the histogram will have bars with heights corresponding to these frequencies: 3, 1, 4, 4, 4 for the classes 93-96, 97-100, 101-104, 105-108, 109-112 respectively.