Male and female populations of humpback whales under 80 years old are shown below by age: 




Age: 0-9; Male: 15; Female: 5

age: 10-16; Male: 13; female: 9

Age: 20-29; Male: 13; Female: 13

Age: 30-39; Male: 16; females 15 

age: 40-49; Male: 22; female: 24

Age: 50-59; male: 24; female: 23

Age: 60-69; male: 15; female: 17

Age: 70-79; male: 15; female: 12




Approximate the population mean and standard deviation for both male and female. 

To approximate the population mean and standard deviation for both male and female humpback whales, we'll follow these steps:

### Steps:

1. **Calculate the Midpoint for Each Age Interval:**
   \[
   \text{Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}
   \]

2. **Calculate the Mean for Each Group (Male and Female):**
   \[
   \text{Mean} = \frac{\sum (\text{Midpoint} \times \text{Frequency})}{\sum \text{Frequency}}
   \]

3. **Calculate the Standard Deviation for Each Group (Male and Female):**
   \[
   \text{Standard Deviation} = \sqrt{\frac{\sum \left[(\text{Midpoint} - \text{Mean})^2 \times \text{Frequency}\right]}{\sum \text{Frequency}}}
   \]

### Data:

| Age Interval (Years) | Midpoint (Years) | Male Frequency | Female Frequency |
|----------------------|------------------|----------------|------------------|
| 0-9                  | 4.5              | 15             | 5                |
| 10-19                | 15.5             | 13             | 9                |
| 20-29                | 24.5             | 13             | 13               |
| 30-39                | 34.5             | 16             | 15               |
| 40-49                | 44.5             | 22             | 24               |
| 50-59                | 54.5             | 24             | 23               |
| 60-69                | 64.5             | 15             | 17               |
| 70-79                | 74.5             | 15             | 12               |

### Now, let's calculate the mean and standard deviation for both male and female populations.The approximate population statistics for male and female humpback whales under 80 years old are as follows:

- **Male Population:**
  - Mean age: **41.44 years**
  - Standard deviation: **21.66 years**

- **Female Population:**
  - Mean age: **45.00 years**
  - Standard deviation: **18.90 years**

Would you like further details or have any other questions?

Here are some related questions you might consider:
1. How does the difference in mean age between males and females impact the population dynamics?
2. What does the standard deviation tell us about the age distribution of male and female whales?
3. How would the mean and standard deviation change if we included whales aged 80 and above?
4. What could be the biological implications of the differences in age distribution between males and females?
5. How could these statistics help in understanding the longevity and survival rates of humpback whales?

**Tip:** Understanding the standard deviation is crucial for interpreting the variability in the data. A lower standard deviation means the ages are more clustered around the mean, while a higher standard deviation indicates a wider age spread.

Learn how to calculate the approximate population mean and standard deviation for male and female humpback whales under 80 years old. This problem involves statistical analysis including mean and standard deviation calculations based on age and population data.

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