Question

here are the hottest recorded temperatures (in °f) for each of fifteen cities throughout north america.
temperatures
(in °f)
111 106 117 108 98
103 102 108 104 105
108 110 112 114 100
(a) complete the grouped frequency distribution for
the data. (note that the class width is 5.)
temperatures
(in °f)
frequency
97.5-102.5
102.5-107.5
107.5-112.5
112.5-117.5
(b) construct a histogram for the data.
frequency
7
6
5
4
3
2
1
0
97.5 102.5 107.5 112.5 117.5
temperatures (in °f)

Explanation:

Step1: Analyze class 97.5 - 102.5

Check which data points lie in this interval. The data points are 98, 102, 100. So count them: 3 values.

Step2: Analyze class 102.5 - 107.5

Data points: 103, 104, 105, 106. Count: 4 values.

Step3: Analyze class 107.5 - 112.5

Data points: 111, 108, 108, 108, 110, 112. Count: 6 values.

Step4: Analyze class 112.5 - 117.5

Data points: 114, 117. Count: 2 values.

For part (b), the histogram will have bars with heights equal to the frequencies found: 3 for 97.5 - 102.5, 4 for 102.5 - 107.5, 6 for 107.5 - 112.5, and 2 for 112.5 - 117.5.

Answer:

(for part a frequencies):
97.5 - 102.5: 3
102.5 - 107.5: 4
107.5 - 112.5: 6
112.5 - 117.5: 2

(For part b, the histogram bars will have these heights corresponding to each class interval on the x - axis.)