Math Problem Statement
Weight_(g) Frequency
6.000-6.049 3
6.050-6.099 4
6.100-6.149 7
6.150-6.199 12
6.200-6.249 11
6.250-6.299 6
6.300-6.349 4
6.350-6.399 1 Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?
Solution
To answer this question, we will follow these steps:
1. Construct the Histogram:
- The histogram is based on the weight ranges (classes) and the corresponding frequencies.
Weight (g) Range | Frequency |
---|---|
6.000-6.049 | 3 |
6.050-6.099 | 4 |
6.100-6.149 | 7 |
6.150-6.199 | 12 |
6.200-6.249 | 11 |
6.250-6.299 | 6 |
6.300-6.349 | 4 |
6.350-6.399 | 1 |
We can now visualize this in a histogram. Since I cannot plot directly here, let me describe how it would look:
- X-axis: This will show the weight ranges (6.000-6.049, 6.050-6.099, etc.).
- Y-axis: This will show the frequency (number of occurrences in each range).
- The bars would rise to heights based on the frequency of each weight class.
2. Does the histogram depict data that have a normal distribution?
A normal distribution generally exhibits a bell-shaped curve, where:
- Most of the data falls around the central value.
- The frequencies taper off symmetrically towards the lower and upper ends.
Based on the frequencies:
- The highest frequency (12) occurs in the 6.150-6.199 range, which is near the center.
- Frequencies decrease as we move towards the lower (6.000-6.049) and upper (6.350-6.399) classes.
The distribution appears roughly symmetric around the center, showing some characteristics of a normal distribution but not perfectly so. There is a slight skew towards the higher weights (the right-hand side frequencies taper off slower than the left).
Conclusion:
The histogram somewhat resembles a normal distribution, but the slight skew on the right-hand side suggests that it may not perfectly follow the characteristics of a normal distribution. It’s not perfectly bell-shaped and symmetric.
Would you like to see a detailed explanation of normal distributions or a step-by-step guide on constructing histograms?
Here are 5 related questions you might find interesting:
- What are the conditions for a perfectly normal distribution?
- How do we measure skewness in a distribution?
- How can we check for normality using statistical tests?
- What other types of distributions could fit this data?
- How does the sample size affect the appearance of a histogram?
Tip: When analyzing a histogram, observe the symmetry and the spread of the data to determine its distribution type.
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Math Problem Analysis
Mathematical Concepts
Statistics
Frequency Distribution
Histogram
Normal Distribution
Formulas
-
Theorems
Normal Distribution Curve
Skewness in Data Distribution
Suitable Grade Level
Grades 9-12