https://file.aiquickdraw.com/mathbot/file/1727059676600mu795j1z.jpg

Let's solve the problem shown in the image. The task involves calculating the **mean** and **standard deviation** for the male population of humpback whales based on age.

### Table of Data:
| Age Group | Males |
|-----------|-------|
| 0-9       | 12    |
| 10-19     | 10    |
| 20-29     | 15    |
| 30-39     | 20    |
| 40-49     | 25    |
| 50-59     | 24    |
| 60-69     | 20    |
| 70-79     | 15    |

#### Step 1: Calculate the mean age (μ)

We need to approximate the mean using the midpoint of each age range, weighted by the population of males in that range.

- **Midpoints** of the age groups:
  - 0-9: 4.5
  - 10-19: 14.5
  - 20-29: 24.5
  - 30-39: 34.5
  - 40-49: 44.5
  - 50-59: 54.5
  - 60-69: 64.5
  - 70-79: 74.5

#### Step 2: Calculate the weighted mean

We can calculate the weighted mean using the formula:

\[
\mu = \frac{\sum (x_i \cdot f_i)}{\sum f_i}
\]

Where:
- \( x_i \) is the midpoint of the age group
- \( f_i \) is the frequency (number of males)

#### Step 3: Calculate the standard deviation (σ)

Once we have the mean, the standard deviation is calculated using:

\[
\sigma = \sqrt{\frac{\sum f_i (x_i - \mu)^2}{\sum f_i}}
\]

Let me now calculate these values.The approximate **mean age** of the male humpback whale population is **43.15 years**. The **standard deviation** is approximately **20.60 years**.

Do you need more details or have any further questions?

Here are 5 related questions for further exploration:
1. How would you calculate the mean for the female humpback whale population?
2. How do weighted means differ from regular means?
3. What is the importance of standard deviation in interpreting data spread?
4. How would the results change if one age group had a significantly higher population?
5. Can you apply this method to other types of population data?

**Tip:** When calculating a weighted mean, always ensure that the weights (frequencies) correctly reflect the importance or size of each group.

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

Learn how to calculate the population mean and standard deviation for the male population of humpback whales under 80 years old, based on age groups. This problem involves key statistical concepts like weighted averages and variance, making it ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation