Use the following frequency table of weights of boxes (in pounds) to answer the questions below. Remember to keep one more decimal place than what is in your data.

 

Class	Frequency
1.0 - 3.4	2
3.5 - 5.9	5
6.0 - 8.4	7
8.5 - 10.9	16
11.0 - 13.4	4
Question 7 (4 points) 

Listen
Estimate the mean of the data using the Frequency Distribution.

Your Answer:
Question 7 options:
Answer	units
Question 8 (4 points) 

Listen
What are the class midpoints?

Question 8 options:

2.2, 4.7, 7.2, 9.7, 12.2


3.5, 6, 11.5, 10


2.25, 4.75, 7.25, 9.75, 12.25


0.95, 3.45, 5.95, 8.45, 10.95, 13.45

Question 9 (2 points) 

Listen
What is the shape of the distribution?

Question 9 options:

skewed to the right


skewed to the left


uniform


symmetric



Let's go through each question step by step:

### **Question 7: Estimate the mean of the data using the frequency distribution**

To estimate the mean, we need to calculate the midpoint of each class, multiply it by the class frequency, sum those products, and divide by the total number of observations.

1. **Class midpoints** (based on the intervals):
    - Midpoint of 1.0 - 3.4: \( \frac{1.0 + 3.4}{2} = 2.2 \)
    - Midpoint of 3.5 - 5.9: \( \frac{3.5 + 5.9}{2} = 4.7 \)
    - Midpoint of 6.0 - 8.4: \( \frac{6.0 + 8.4}{2} = 7.2 \)
    - Midpoint of 8.5 - 10.9: \( \frac{8.5 + 10.9}{2} = 9.7 \)
    - Midpoint of 11.0 - 13.4: \( \frac{11.0 + 13.4}{2} = 12.2 \)

2. **Total number of observations**: \( 2 + 5 + 7 + 16 + 4 = 34 \)

3. **Calculating the mean**:
\[
\text{Mean} = \frac{(2.2 \times 2) + (4.7 \times 5) + (7.2 \times 7) + (9.7 \times 16) + (12.2 \times 4)}{34}
\]
Let's compute the result.

I'll calculate this for you.The estimated mean of the data using the frequency distribution is approximately **8.30 pounds**.

---

### **Question 8: What are the class midpoints?**

The class midpoints were calculated as:
\[
2.2, 4.7, 7.2, 9.7, 12.2
\]
This corresponds to the answer option:
- **2.2, 4.7, 7.2, 9.7, 12.2**

---

### **Question 9: What is the shape of the distribution?**

Looking at the frequencies, we notice:
- The distribution has a higher frequency for the class 8.5 - 10.9, with a gradual decrease afterward, which suggests that the data has a longer tail to the left (lower values), but fewer on the right (higher values).

Thus, the distribution is **skewed to the left**.

---

Would you like any further details or clarification?

### Relative questions:
1. How do you compute the median from a frequency distribution?
2. What would the variance of this frequency distribution be?
3. How do you calculate the mode from grouped data like this?
4. What are the effects of skewness on measures of central tendency?
5. How can you identify a normal distribution using a frequency table?

### Tip:
When estimating the mean from grouped data, using more precise class midpoints improves the accuracy of your estimate.

Use the following frequency table of weights of boxes (in pounds) to answer the questions below. Estimate the mean of the data using the Frequency Distribution. What are the class midpoints? What is the shape of the distribution?

Learn how to estimate the mean and identify the shape of a distribution using a frequency table of weights. This problem covers key concepts such as frequency distribution, class midpoints, and skewness. Suitable for students in Grades 9-11.

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