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Data was collected for 40 randomly selected trees growing in the median strip of a busy freeway. The height of each tree (in inches) was recorded. Data was recorded to the nearest whole inch. The data is summarized in the histogram below.

2
4
6
8
height (in)
25
30
35
40
45
50
55
60
65
Frequency
[Graphs generated by this script: setBorder(47,40,20,15); initPicture(20.5,65,0,9);axes(128.4,2,1,null,2); fill="blue"; stroke="black"; textabs([165,0],"height (in)","above");line([25,-0.18],[25,0.18]); text([25,0],"25","below");line([30,-0.18],[30,0.18]); text([30,0],"30","below");line([35,-0.18],[35,0.18]); text([35,0],"35","below");line([40,-0.18],[40,0.18]); text([40,0],"40","below");line([45,-0.18],[45,0.18]); text([45,0],"45","below");line([50,-0.18],[50,0.18]); text([50,0],"50","below");line([55,-0.18],[55,0.18]); text([55,0],"55","below");line([60,-0.18],[60,0.18]); text([60,0],"60","below");line([65,-0.18],[65,0.18]); text([65,0],"65","below");textabs([0,115],"Frequency","right",90);rect([25,0],[30,2]);rect([30,0],[35,2]);rect([35,0],[40,9]);rect([40,0],[45,6]);rect([45,0],[50,8]);rect([50,0],[55,9]);rect([55,0],[60,3]);rect([60,0],[65,1]);]

What is the minimum possible tree height for the data recorded for this histogram? Note: Each class contains its lower class boundary, but not its upper class boundary.

1 answer

To determine the minimum possible tree height from the histogram, we first need to understand how the height ranges are represented in the histogram.

According to the histogram description, it consists of intervals that include the lower boundary of each class but not the upper boundary. Based on the given data:

  • The first bar corresponds to the interval \([25, 30)\) and has a frequency of 2.
  • The second bar corresponds to the interval \([30, 35)\) with a frequency of 2.
  • The third bar corresponds to the interval \([35, 40)\) with a frequency of 9.
  • The fourth bar corresponds to the interval \([40, 45)\) with a frequency of 6.
  • The fifth bar corresponds to the interval \([45, 50)\) with a frequency of 8.
  • The sixth bar corresponds to the interval \([50, 55)\) with a frequency of 9.
  • The seventh bar corresponds to the interval \([55, 60)\) with a frequency of 3.
  • The eighth bar corresponds to the interval \([60, 65)\) with a frequency of 1.

Since the lowest height class is \([25, 30)\), the minimum possible tree height is the lower boundary of this class range, which is 25 inches.