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To find the mean weight using the histogram, we need to use the midpoints of each weight class and their corresponding frequencies. Here's the step-by-step process:

### Step 1: Identify the intervals and frequencies from the histogram
From the histogram, we can approximate the following weight intervals and frequencies:

- 100-105 lbs: 1 student
- 105-110 lbs: 1 student
- 110-115 lbs: 2 students
- 115-120 lbs: 3 students
- 120-125 lbs: 5 students
- 125-130 lbs: 8 students
- 130-135 lbs: 6 students
- 135-140 lbs: 2 students
- 140-145 lbs: 1 student
- 145-150 lbs: 0 students
- 150-155 lbs: 1 student

### Step 2: Calculate the midpoints of each interval
The midpoint is the average of the lower and upper bounds of each class interval.

- 100-105 lbs: midpoint = (100 + 105) / 2 = 102.5
- 105-110 lbs: midpoint = (105 + 110) / 2 = 107.5
- 110-115 lbs: midpoint = (110 + 115) / 2 = 112.5
- 115-120 lbs: midpoint = (115 + 120) / 2 = 117.5
- 120-125 lbs: midpoint = (120 + 125) / 2 = 122.5
- 125-130 lbs: midpoint = (125 + 130) / 2 = 127.5
- 130-135 lbs: midpoint = (130 + 135) / 2 = 132.5
- 135-140 lbs: midpoint = (135 + 140) / 2 = 137.5
- 140-145 lbs: midpoint = (140 + 145) / 2 = 142.5
- 145-150 lbs: midpoint = (145 + 150) / 2 = 147.5
- 150-155 lbs: midpoint = (150 + 155) / 2 = 152.5

### Step 3: Multiply the midpoints by the corresponding frequencies
Now, we calculate the product of the midpoint and the frequency for each class:

- 102.5 × 1 = 102.5
- 107.5 × 1 = 107.5
- 112.5 × 2 = 225
- 117.5 × 3 = 352.5
- 122.5 × 5 = 612.5
- 127.5 × 8 = 1020
- 132.5 × 6 = 795
- 137.5 × 2 = 275
- 142.5 × 1 = 142.5
- 147.5 × 0 = 0
- 152.5 × 1 = 152.5

### Step 4: Add up the products
\[
102.5 + 107.5 + 225 + 352.5 + 612.5 + 1020 + 795 + 275 + 142.5 + 0 + 152.5 = 3785.5
\]

### Step 5: Add up the frequencies
The total number of students is 30, as mentioned.

### Step 6: Calculate the mean
\[
\text{Mean} = \frac{\text{Sum of products}}{\text{Total frequency}} = \frac{3785.5}{30} = 126.1833
\]

Thus, the mean weight is approximately **126.183 pounds** (rounded to the nearest thousandth).

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Do you need more details or have any questions?

Here are 5 related questions:
1. What is the difference between mean and median in a data set?
2. How does the shape of a histogram affect the interpretation of data?
3. How would you calculate the median weight from this histogram?
4. Why is it important to use midpoints when calculating the mean from grouped data?
5. How would the calculation change if the intervals had different sizes?

**Tip:** When calculating the mean from a histogram, always remember to use the midpoints of the intervals, as they best represent the data within each range.

The weights (to the nearest five pounds) of 30 randomly selected male college students are organized in the histogram. Use the graph to find the mean weight.

Learn how to calculate the mean weight of 30 male college students using a histogram. This problem involves key statistical concepts such as the use of midpoints and frequencies in grouped data. Suitable for high school students in Grades 10-12.

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