Math Problem Statement
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.
246810height (in)101520253035404550Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(5.5,50,0,11);axes(98.8,2,1,null,2); fill="blue"; stroke="black"; textabs([165,0],"height (in)","above");line([10,-0.22],[10,0.22]); text([10,0],"10","below");line([15,-0.22],[15,0.22]); text([15,0],"15","below");line([20,-0.22],[20,0.22]); text([20,0],"20","below");line([25,-0.22],[25,0.22]); text([25,0],"25","below");line([30,-0.22],[30,0.22]); text([30,0],"30","below");line([35,-0.22],[35,0.22]); text([35,0],"35","below");line([40,-0.22],[40,0.22]); text([40,0],"40","below");line([45,-0.22],[45,0.22]); text([45,0],"45","below");line([50,-0.22],[50,0.22]); text([50,0],"50","below");textabs([0,115],"Frequency","right",90);rect([10,0],[15,1]);rect([15,0],[20,5]);rect([20,0],[25,4]);rect([25,0],[30,11]);rect([30,0],[35,7]);rect([35,0],[40,9]);rect([40,0],[45,1]);rect([45,0],[50,2]);]
Based on this histogram, determing the minimum and maximum possible tree heights for the recorded data. Note: Each class contains its lower class boundary, but not its upper class boundary.
Minimum tree height = Correct inches Maximum tree height = inches
Question HelpQuestion 5:
Video1
Solution
To determine the minimum and maximum possible tree heights based on the provided histogram information, we can analyze the class intervals.
Class Intervals
From the histogram, it seems like the class intervals are as follows:
- 10 - 15 inches
- 15 - 20 inches
- 20 - 25 inches
- 25 - 30 inches
- 30 - 35 inches
- 35 - 40 inches
- 40 - 45 inches
- 45 - 50 inches
Lower and Upper Boundaries
- Minimum Tree Height: The lowest class interval is from 10 to 15 inches. Since the lower class boundary is included, the minimum possible tree height is 10 inches.
- Maximum Tree Height: The highest class interval is from 45 to 50 inches. The upper boundary of this class interval is not included, so the maximum possible tree height would be just below 50 inches. Therefore, the maximum possible height can be approximated as 49.99 inches, but for practical purposes, we can consider it 49 inches.
Summary
- Minimum tree height: 10 inches
- Maximum tree height: 49 inches
Would you like further details or explanations on any aspect of this analysis? Here are a few questions to consider:
- How are class boundaries defined in histograms?
- What other statistical measures can be derived from this data?
- Why is the upper boundary not included in class intervals?
- How can this data be used in ecological studies?
- What might be the implications of tree height in an urban environment?
Tip: When working with histograms, always clarify the inclusion/exclusion of class boundaries to accurately interpret the data.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Statistics
Data Analysis
Histograms
Formulas
Class Boundaries Interpretation in Histograms
Theorems
Class Boundary Theorem
Suitable Grade Level
Grades 9-12