Below are the weights (in pounds) of 9 randomly selected thirteen-year old girls
 
Weights (pounds): 87, 94, 93, 119, 96, 90, 123, 98, 139
 
Find the standard deviation for the weights of the thirteen-year old girls.

To find the standard deviation for the weights of the thirteen-year-old girls, we will use the following steps:

### 1. Calculate the Mean
The mean (\(\mu\)) is calculated by summing all the values and dividing by the number of data points.

\[
\mu = \frac{\sum X_i}{N}
\]

where \(X_i\) are the individual weights and \(N\) is the number of data points.

### 2. Calculate the Variance
The variance (\(\sigma^2\)) is calculated as the average of the squared differences from the Mean:

\[
\sigma^2 = \frac{\sum (X_i - \mu)^2}{N}
\]

### 3. Calculate the Standard Deviation
The standard deviation (\(\sigma\)) is the square root of the variance:

\[
\sigma = \sqrt{\sigma^2}
\]

Let's calculate the standard deviation for the weights.The standard deviation for the weights of the thirteen-year-old girls is approximately **17.05 pounds**.

Would you like more details or have any questions?

---

Here are some related questions:
1. How is standard deviation used to measure variability in a data set?
2. What is the difference between population and sample standard deviation?
3. How does the standard deviation relate to the normal distribution?
4. Why might some data sets have a higher standard deviation than others?
5. How does the mean affect the standard deviation?
6. What role does standard deviation play in statistical inference?
7. Can standard deviation be negative?
8. How can standard deviation be interpreted in the context of real-world data?

**Tip:** Standard deviation is a crucial measure of spread, indicating how much the data points deviate from the mean. A higher standard deviation means more variability in the data.

Learn how to calculate the standard deviation for a set of weights of thirteen-year-old girls using statistical methods. This problem involves computing the mean, variance, and standard deviation, providing a practical application of descriptive statistics. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation