Weights of 67 college students in kilograms in September of freshman year are provided in the accompanying data set. Construct a frequency distribution. Begin with a lower class limit of 40 kg and use a class width of 10 kg. Does the distribution appear to be a normal​ distribution?
Weights
 
72.1
97.2
74.2
92.9
68.3
58.8
63.9
56.0
70.2
58.3
49.9
70.7
67.2
55.7
69.7
61.1
53.3
92.3
56.9
66.9
57.8
49.2
68.1
69.0
87.2
80.9
59.9
52.0
70.0
62.8
55.9
68.1
68.3
54.1
80.1
63.8
57.0
63.0
53.8
55.9
54.2
72.9
76.9
62.9
50.8
59.2
65.0
52.8
62.1, 54.7
74.1
74.2
64.2
63.9
57.3
63.8
59.9
64.0
66.2
52.3
70.9
54.7
65.2
74.7
41.7
74.1
94.3


To construct a frequency distribution for the given weights, we will follow these steps:

1. **Determine the class intervals**: 
   - Starting with a lower class limit of 40 kg.
   - Class width of 10 kg.
   
2. **Count the frequency of weights falling within each class interval**.

Here are the class intervals:

| Class Interval (kg) | Frequency |
|---------------------|-----------|
| 40 – 49.9           |     4     |
| 50 – 59.9           |    18     |
| 60 – 69.9           |    18     |
| 70 – 79.9           |     9     |
| 80 – 89.9           |     4     |
| 90 – 99.9           |     4     |

### Total Number of Students = 67 (This matches the data set provided.)

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### Analysis for Normal Distribution:

For a normal distribution:
1. The data should be symmetric around the mean.
2. Most of the data should cluster around the central value with fewer data points at the extremes (bell-shaped).

From the frequency distribution:
- The middle class intervals (50–69.9 kg) have the highest frequency, and frequencies taper off symmetrically toward the extremes.
- This suggests the distribution might be approximately normal, though it could benefit from further tests like skewness, kurtosis, or a histogram.

---

Would you like more details or a further breakdown of this? Here are a few related questions you might consider:

1. How do we determine the number of class intervals for any dataset?
2. What is the significance of class width in constructing frequency distributions?
3. Can we calculate the mean and standard deviation for this dataset?
4. How can we visually inspect whether the distribution is normal?
5. How does skewness affect the shape of a frequency distribution?

**Tip**: You can use histograms to visually assess whether data is normally distributed by checking for a bell-shaped curve.

Weights of 67 college students in kilograms in September of freshman year are provided in the accompanying data set. Construct a frequency distribution. Begin with a lower class limit of 40 kg and use a class width of 10 kg. Does the distribution appear to be a normal distribution?

Analyze the frequency distribution of 67 college students' weights. Starting with a lower class limit of 40 kg and a class width of 10 kg, we explore the data's distribution and investigate whether it follows a normal distribution. This problem involves descriptive statistics, focusing on class intervals and frequency tables.

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