Question

(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
↑
6
5
4
3
2
1
0
107 116 100 100 100
111 106 114 117 112
103 109 105 104 98

Explanation:

Step1: Count data in first range

Count numbers in 97.5 - 102.5. The numbers are 100, 100, 100, 103, 98. So the frequency is 5.

Step2: Count data in second range

Count numbers in 102.5 - 107.5. The numbers are 107, 106, 105, 104. So the frequency is 4.

Step3: Count data in third range

Count numbers in 107.5 - 112.5. The numbers are 111, 112. So the frequency is 2.

Step4: Count data in fourth range

Count numbers in 112.5 - 117.5. The numbers are 116, 114, 117. So the frequency is 3.

Step5: Construct histogram

On the x - axis, label the temperature ranges (97.5 - 102.5, 102.5 - 107.5, 107.5 - 112.5, 112.5 - 117.5). On the y - axis, label the frequency. Draw bars with heights corresponding to the frequencies (5, 4, 2, 3 respectively).

Answer:

(a)

Temperatures (in °F)	Frequency
102.5 - 107.5	4
107.5 - 112.5	2
112.5 - 117.5	3

(b) Histogram constructed with x - axis as temperature ranges and y - axis as frequency with bar - heights 5, 4, 2, 3 for respective ranges.