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: 15; female: 10
Age: 20-29; Male: 13; Female: 17
Age: 30-39; Male: 17; females 17
age: 40-49; Male: 23; female: 22
Age: 50-59; male: 23; female: 25
Age: 60-69; male: 15; female: 20
Age: 70-79; male: 13; female: 12

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

To calculate the population mean and standard deviation for both the male and female humpback whale populations under 80 years old, we'll go through the following steps:

1. **Find the mean** for each gender's population.
2. **Calculate the variance** (average of the squared differences from the mean).
3. **Find the standard deviation**, which is the square root of the variance.

We will treat each age group as equally represented in the population, assuming each individual whale is independent of others in terms of age distribution. The midpoints of the age ranges can be used as the "age" for each group.

Given dataTo calculate the population mean and standard deviation for both the male and female humpback whale populations under 80 years old, we'll go through the following steps:

1. **Find the mean** for each gender's population.
2. **Calculate the variance** (average of the squared differences from the mean).
3. **Find the standard deviation**, which is the square root of the variance.

We will treat each age group as equally represented in the population, assuming each individual whale is independent of others in terms of age distribution. The midpoints of the age ranges can be used as the "age" for each group.

Given 

| Age Range | Male Population | Female Population |
|-----------|-----------------|-------------------|
| 0-9       | 15              | 5                 |
| 10-19     | 15              | 10                |
| 20-29     | 13              | 17                |
| 30-39     | 17              | 17                |
| 40-49     | 23              | 22                |
| 50-59     | 23              | 25                |
| 60-69     | 15              | 20                |
| 70-79     | 13              | 12                |

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

- **Male Population:**
  - Mean: 16.75
  - Standard Deviation: 3.80

- **Female Population:**
  - Mean: 16.00
  - Standard Deviation: 6.20

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How does the population distribution vary across age ranges for males and females?
2. What factors could explain the differences in standard deviation between male and female populations?
3. How would the inclusion of whales older than 80 impact the statistics?
4. What would be the overall mean and standard deviation if male and female populations were combined?
5. How might the populations differ geographically or seasonally?

**Tip:** Standard deviation helps to understand the spread of the data. A higher standard deviation indicates more variability in the population.

Learn how to calculate the population mean and standard deviation for male and female humpback whale populations under 80 years old. This problem involves descriptive statistics, including mean calculation, variance, and standard deviation. Suitable for advanced high school or college-level students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation