Question

the data set provided below provides the heights in feet of 31 felled black cherry trees. 71 64 64 72 81 82 64 73 80 77 78 78 78 68 73 74 85 86 71 65 76 79 73 72 77 79 84 78 82 82 85 1. complete the frequency distribution for the data. height frequency 60,65) 65,70) 70,75) 75,80) 80,85) 85,90) 2. which of the following is the correct histogram for this data?

Explanation:

Step1: Count values in [60,65)

Count the number of values in the dataset that are greater than or equal to 60 and less than 65. There are 3 (64, 64, 64).

Step2: Count values in [65,70)

Count the number of values in the dataset that are greater than or equal to 65 and less than 70. There are 2 (68, 65).

Step3: Count values in [70,75)

Count the number of values in the dataset that are greater than or equal to 70 and less than 75. There are 7 (71, 73, 73, 74, 71, 73, 72).

Step4: Count values in [75,80)

Count the number of values in the dataset that are greater than or equal to 75 and less than 80. There are 11 (78, 78, 78, 75, 76, 79, 77, 79, 78, 77, 78).

Step5: Count values in [80,85)

Count the number of values in the dataset that are greater than or equal to 80 and less than 85. There are 6 (82, 80, 82, 84, 82, 85).

Step6: Count values in [85,90)

Count the number of values in the dataset that are greater than or equal to 85 and less than 90. There are 2 (86, 85).

Answer:

Height	Frequency
[65,70)	2
[70,75)	7
[75,80)	11
[80,85)	6
[85,90)	2

To determine the correct histogram, we note that the frequencies match the third histogram (from the top - has frequencies 3, 2, 7, 11, 6, 2 for the respective intervals). So the answer for part 2 is the third histogram.