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approximate the population mean and standard deviation of age for males

To approximate the population mean and standard deviation of the age for the male tortoises, we need to perform the following steps:

1. **Calculate the Mean**:
   The mean is calculated using the formula:
   \[
   \mu = \frac{\sum (x \cdot f)}{\sum f}
   \]
   where:
   - \( x \) is the midpoint of each age group.
   - \( f \) is the frequency of males in each age group.

2. **Calculate the Standard Deviation**:
   The standard deviation is calculated using the formula:
   \[
   \sigma = \sqrt{\frac{\sum (f \cdot (x - \mu)^2)}{\sum f}}
   \]

We will first calculate the midpoints, then use them to find the mean and standard deviation.

### Age Groups and Corresponding Frequencies for Males:

| Age Group | Midpoint (\(x\)) | Frequency (\(f\)) |
|-----------|------------------|-------------------|
| 0-9       | \( \frac{0 + 9}{2} = 4.5 \)  | 13               |
| 10-19     | \( \frac{10 + 19}{2} = 14.5 \) | 16              |
| 20-29     | \( \frac{20 + 29}{2} = 24.5 \) | 15              |
| 30-39     | \( \frac{30 + 39}{2} = 34.5 \) | 19              |
| 40-49     | \( \frac{40 + 49}{2} = 44.5 \) | 22              |
| 50-59     | \( \frac{50 + 59}{2} = 54.5 \) | 25              |
| 60-69     | \( \frac{60 + 69}{2} = 64.5 \) | 18              |
| 70-79     | \( \frac{70 + 79}{2} = 74.5 \) | 12              |

Next, I will calculate the mean and standard deviation.The population mean age for the male tortoises is approximately **40.79 years**, and the standard deviation is approximately **20.99 years**.

Would you like further details or have any questions?

Here are 5 related questions you might find useful:
1. How would the mean and standard deviation change for the female population?
2. What is the significance of the standard deviation in this context?
3. How can we interpret the age distribution based on this data?
4. Can we calculate the median age for the male tortoises from this data?
5. What is the combined population mean and standard deviation for both males and females?

**Tip**: The larger the standard deviation, the more spread out the data is around the mean.

Approximate the population mean and standard deviation of age for male tortoises.

Learn how to calculate the population mean and standard deviation of age for male tortoises, based on given age groups and population data. This includes a step-by-step approach to calculating midpoints, frequencies, and applying statistical formulas.

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