Math Problem Statement
1015913172125dataFrequency[Graphs generated by this script: setBorder(54,40,20,5); initPicture(0,25,0,10);axes(1000,2,1,1000,2); fill="blue"; stroke="black";line([1,-0.2],[1,0.2]); text([1,0],"1","below");line([5,-0.2],[5,0.2]); text([5,0],"5","below");line([9,-0.2],[9,0.2]); text([9,0],"9","below");line([13,-0.2],[13,0.2]); text([13,0],"13","below");line([17,-0.2],[17,0.2]); text([17,0],"17","below");line([21,-0.2],[21,0.2]); text([21,0],"21","below");line([25,-0.2],[25,0.2]); text([25,0],"25","below");textabs([165,0],"data","above");textabs([0,115],"Frequency","right",90);rect([1,0],[5,10]);rect([5,0],[9,4]);rect([9,0],[13,3]);rect([13,0],[17,7]);rect([17,0],[21,2]);rect([21,0],[25,9]);]
Based on the histogram above, what is the class width?
Class width =
What is the sample size?
Sample size =
Solution
To solve this, we'll break down the details from the histogram.
1. Class Width:
- Class Width is the difference between the lower bounds of two consecutive classes.
- From the code, the classes are defined by the ranges:
- [1, 5], [5, 9], [9, 13], [13, 17], [17, 21], [21, 25]
The class width can be calculated as:
So, the Class Width = 4.
2. Sample Size:
- The sample size is the total frequency of all classes.
- From the code, the frequencies are:
- [1, 5] → 10
- [5, 9] → 4
- [9, 13] → 3
- [13, 17] → 7
- [17, 21] → 2
- [21, 25] → 9
Summing these values:
So, the Sample Size = 35.
Summary:
- Class Width = 4
- Sample Size = 35
Do you want more details or have any questions?
Here are 5 related questions you could explore:
- How would the histogram change if the class width was decreased?
- What is the relative frequency of the largest class?
- How do you interpret the mode from this histogram?
- What would be the impact of adding more data points on the histogram?
- How could we normalize this histogram?
Tip: Always check the class boundaries carefully when interpreting histograms!
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Math Problem Analysis
Mathematical Concepts
Statistics
Histograms
Class Width
Sample Size
Formulas
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Theorems
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Suitable Grade Level
Undergraduate