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?
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72.1
97.3
74.2
92.8
68.3
59.1
64.1
56.1
70.0
57.9
50.0
70.9
67.1
56.2
70.1
61.1
52.8
91.7
56.9
67.1
58.1
49.2
67.9
69.1
86.9
80.8
60.2
51.8
69.8
62.8
55.8
67.8
68.1
54.2
80.2
64.1 57.1
63.1
54.3
55.9
53.8
72.8
77.2
62.9
51.0
58.9
64.9
52.8
62.0
55.2
74.3
73.9
64.3
64.3
57.0
64.0
60.3
63.7
66.1
51.7
70.8
54.8
65.2
74.8
42.2
73.9
94.1

To construct a frequency distribution, we need to:

1. Define the class intervals based on the provided lower class limit of 40 kg and a class width of 10 kg.
2. Tally the number of weights that fall within each class interval.

### Steps:

1. **Class Intervals**: Starting from 40 kg with a class width of 10 kg, we create intervals:  
   - 40–49.9 kg  
   - 50–59.9 kg  
   - 60–69.9 kg  
   - 70–79.9 kg  
   - 80–89.9 kg  
   - 90–99.9 kg

2. **Tally the data**: Count the number of weights in each class interval from the given data set.

### Frequency Distribution Table:

| Class Interval | Frequency (Number of Students) |
|----------------|-------------------------------|
| 40–49.9 kg     | 4                             |
| 50–59.9 kg     | 17                            |
| 60–69.9 kg     | 18                            |
| 70–79.9 kg     | 12                            |
| 80–89.9 kg     | 4                             |
| 90–99.9 kg     | 4                             |

### Does the distribution appear normal?

A **normal distribution** generally has a bell-shaped curve, where the frequency is highest in the middle class intervals and tapers off symmetrically towards the lower and higher classes. Here, the middle class (60–69.9 kg) has the highest frequency, and the distribution tapers off on both sides, indicating a roughly symmetric distribution.

So, the distribution **roughly approximates a normal distribution**, though it may not be perfectly symmetrical.

Would you like more details on this or a graphical representation of the frequency distribution?

Here are 5 related questions:

1. How do you construct a histogram from a frequency distribution?
2. What are the characteristics of a normal distribution?
3. What is class width and how is it determined?
4. How can we check for skewness in a distribution?
5. What are other methods to check for normality besides visual inspection?

**Tip**: When analyzing distributions, look at both the symmetry and the central tendency to better understand its shape!

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?

Construct a frequency distribution for the weights of 67 college students, beginning with a lower class limit of 40 kg and using a class width of 10 kg. Analyze whether the distribution approximates a normal distribution, with detailed step-by-step explanation. Suitable for students in Grades 10-12.

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