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From the image provided, you are working on a statistics problem involving the male and female populations of humpback whales under 80 years old. Specifically, you are tasked with calculating the population mean (\( \mu \)) and standard deviation (\( \sigma \)) for both males and females in different age groups.

Here’s how you would approach each part:

1. **Part (a)**: Approximate the population mean and standard deviation of age for males.
   - The answer for the population mean is already given as \( \mu = 43.15 \) and standard deviation \( \sigma = 20.60 \) for males.

2. **Part (b)**: Approximate the population mean and standard deviation of age for females.
   - This is still left to be calculated.

To calculate the **mean** and **standard deviation** for the females, follow these steps:

### 1. Mean of Female Population:
   The mean can be found using the formula:
   \[
   \mu = \frac{\sum (x_i \cdot f_i)}{\sum f_i}
   \]
   where:
   - \( x_i \) is the midpoint of each age group.
   - \( f_i \) is the frequency (number of females in each age group).

### 2. Standard Deviation of Female Population:
   The standard deviation is given by:
   \[
   \sigma = \sqrt{\frac{\sum f_i \cdot (x_i - \mu)^2}{\sum f_i}}
   \]

Would you like me to calculate the mean and standard deviation for the female population based on the data in the table?

Feel free to ask if you have any questions. Here are five relative questions that expand on this problem:

1. How do you determine the midpoints of age groups when calculating the mean?
2. What is the difference between population standard deviation and sample standard deviation?
3. Why do we use midpoints in grouped data for these calculations?
4. How would the results change if you had an unequal population in each group?
5. Can the standard deviation ever be larger than the mean?

**Tip**: Remember that the mean is sensitive to all values in the dataset, while the standard deviation tells you how spread out those values are from the mean.

Male and female populations of humpback whales under 80 years old are represented by the table below. Approximate the population mean and standard deviation of age for males (given) and females.

Learn how to approximate the population mean and standard deviation for both males and females of humpback whales under 80 years old. This problem uses key statistical formulas for grouped data, including calculating the mean and standard deviation. Suitable for college-level statistics.

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