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?

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.

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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.

Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal​ distribution? Why or why​ not?

Learn how to construct a histogram using the given frequency distribution and determine whether the data depicts a normal distribution. This guide explains key statistical concepts such as frequency distributions, histograms, and normal distribution characteristics. Suitable for students in Grades 9-12.

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