Determine if the frequency distribution has Normal distribution or not.

Ages	Number of students
15-18	12
19-22	11
23-26	14
27-30	13
31-34	14
35-38	17
Approximately Normal
Not Normal


To determine if the given frequency distribution has a Normal distribution, we need to assess whether the data fits the characteristics of a normal distribution. A normal distribution typically has the following features:

1. **Symmetry**: The distribution should be roughly symmetric around the mean.
2. **Unimodal**: There should be a single peak in the distribution.
3. **Bell-shaped curve**: The frequencies should gradually decrease as we move away from the central value.

Let's examine the dataTo determine if the given frequency distribution has a Normal distribution, we need to assess whether the data fits the characteristics of a normal distribution. A normal distribution typically has the following features:

1. **Symmetry**: The distribution should be roughly symmetric around the mean.
2. **Unimodal**: There should be a single peak in the distribution.
3. **Bell-shaped curve**: The frequencies should gradually decrease as we move away from the central value.

Let's examine the 

| Ages  | Number of students |
|-------|--------------------|
| 15-18 | 12                 |
| 19-22 | 11                 |
| 23-26 | 14                 |
| 27-30 | 13                 |
| 31-34 | 14                 |
| 35-38 | 17                 |

### Analysis:

1. **Symmetry**: 
   - The distribution is not perfectly symmetric, but it shows some symmetry around the central age groups (23-26, 27-30, 31-34).

2. **Unimodal**:
   - The distribution has a peak in the age group 35-38 (17 students), and it gradually increases towards this peak from both sides.

3. **Bell-shaped curve**:
   - The frequency distribution shows a bell-shaped curve but not a perfect one. The peak occurs at the older age group (35-38), which might suggest a slight skewness to the right.

### Conclusion:
While the distribution does exhibit some characteristics of a normal distribution, such as a roughly bell-shaped curve and unimodality, it is not perfectly symmetric and appears slightly skewed to the right. Therefore, it is **approximately normal** but not perfectly normal.

So, the correct option is **Approximately Normal**.

Would you like more details on this analysis or have any other questions?

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Here are five related questions for further exploration:

1. How can we quantify the skewness of this distribution?
2. What methods are used to test the normality of a distribution statistically?
3. How does the mean and median help in identifying skewness in a distribution?
4. What are the implications of a distribution being approximately normal in statistical analysis?
5. How would a histogram of this data look, and how could it help in identifying normality?

**Tip:** When analyzing distributions, always check for symmetry, unimodality, and whether the data forms a bell-shaped curve to assess normality visually.

Explore how to determine if a frequency distribution exhibits a normal distribution. Analyze data on student ages to assess symmetry, unimodality, and bell-shaped curve characteristics. Suitable for higher education students and statistical analysts.

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