Math Problem Statement
2 4 6 8 1 4 7 10 13 16 19 data Frequency [Graphs generated by this script: setBorder(47,40,20,5); initPicture(0,19,0,9);axes(1000,2,1,1000,2); fill="blue"; stroke="black";line([1,-0.18],[1,0.18]); text([1,0],"1","below");line([4,-0.18],[4,0.18]); text([4,0],"4","below");line([7,-0.18],[7,0.18]); text([7,0],"7","below");line([10,-0.18],[10,0.18]); text([10,0],"10","below");line([13,-0.18],[13,0.18]); text([13,0],"13","below");line([16,-0.18],[16,0.18]); text([16,0],"16","below");line([19,-0.18],[19,0.18]); text([19,0],"19","below");textabs([165,0],"data","above");textabs([0,115],"Frequency","right",90);rect([1,0],[4,7]);rect([4,0],[7,9]);rect([7,0],[10,3]);rect([10,0],[13,2]);rect([13,0],[16,4]);rect([16,0],[19,6]);]
Based on the histogram above, what is the class width?
Class width =
What is the sample size?
Solution
To determine the class width and sample size from the histogram based on the given information, we follow these steps:
1. Class Width
The class width is the difference between the lower boundaries (or the upper boundaries) of consecutive classes.
From the information provided:
- The first class is from 1 to 4
- The second class is from 4 to 7
- The third class is from 7 to 10, and so on.
To find the class width, subtract the lower boundary of the first class from the lower boundary of the second class:
2. Sample Size
The sample size is the total frequency, which is the sum of all the frequencies for each class.
The frequencies provided (as per the rectangles' heights) are:
- First class (1 to 4): Frequency = 7
- Second class (4 to 7): Frequency = 9
- Third class (7 to 10): Frequency = 3
- Fourth class (10 to 13): Frequency = 2
- Fifth class (13 to 16): Frequency = 4
- Sixth class (16 to 19): Frequency = 6
Adding these frequencies gives the total sample size:
Final Answers:
- Class width = 3
- Sample size = 31
Do you want more details or have any questions?
Related Questions:
- How would the histogram look if the class width were 5 instead of 3?
- What would happen to the sample size if one of the frequencies increased by 5?
- How do you interpret the shape of this histogram in terms of data distribution?
- How can you determine the mode from this histogram?
- How would you calculate the relative frequency for each class in this histogram?
Tip:
When interpreting histograms, always start by identifying the class intervals and their frequencies; this will help you quickly understand the distribution of your data.
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Math Problem Analysis
Mathematical Concepts
Statistics
Histograms
Frequency Distribution
Formulas
Class width = Upper boundary of a class - Lower boundary of the previous class
Sample size = Sum of all frequencies
Theorems
None specific; general principles of statistical data representation
Suitable Grade Level
Grades 6-8