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) RangeFrequency
6.000-6.0493
6.050-6.0994
6.100-6.1497
6.150-6.19912
6.200-6.24911
6.250-6.2996
6.300-6.3494
6.350-6.3991

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:

  1. What are the conditions for a perfectly normal distribution?
  2. How do we measure skewness in a distribution?
  3. How can we check for normality using statistical tests?
  4. What other types of distributions could fit this data?
  5. 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