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The problem involves calculating four statistical measures based on the following pendulum period measurements: 3.3 s, 3.4 s, 3.2 s, 3.5 s, and 3.1 s. Let's go through each part step by step.

### a.) Mean
The mean (average) is calculated by summing all the measurements and dividing by the number of measurements:

\[
\text{Mean} = \frac{3.3 + 3.4 + 3.2 + 3.5 + 3.1}{5}
\]

### b.) Variance
The variance measures how far each number in the set is from the mean. It is calculated as:

\[
\text{Variance} = \frac{(x_1 - \text{Mean})^2 + (x_2 - \text{Mean})^2 + \dots + (x_n - \text{Mean})^2}{n}
\]

Where \(x_1, x_2, \dots, x_n\) are the data points, and \(n\) is the number of data points.

### c.) Standard Deviation
The standard deviation is the square root of the variance:

\[
\text{Standard Deviation} = \sqrt{\text{Variance}}
\]

### d.) Measured Period
The measured period is simply the mean of the measurements.

Let me calculate all these values.Here are the calculated values:

a.) **Mean**: 3.3 seconds  
b.) **Variance**: 0.02 seconds²  
c.) **Standard Deviation**: 0.1414 seconds  
d.) **Measured Period**: The measured period is the same as the mean, which is 3.3 seconds.

Let me know if you need further details or explanations.

Here are five related questions to deepen your understanding:

1. How does the variance help in understanding the spread of data?
2. Why is standard deviation often preferred over variance when interpreting data?
3. Can the mean of the measurements be affected by outliers?
4. How would these statistical measures change if we added more data points?
5. What is the significance of calculating these values in physics experiments?

**Tip:** Always remember that variance is in squared units, which is why standard deviation is often used to keep the units consistent with the data itself.

During an experiment in a physics laboratory class, a group of five students was asked to measure the period of a simple pendulum. The measurements were as follows: 3.3s, 3.4s, 3.2s, 3.5s, and 3.1s. Determine the a.) mean, b.) variance, c.) standard deviation, and d.) measured period of the pendulum.

Calculate the mean, variance, and standard deviation for the period of a simple pendulum based on five measurements: 3.3s, 3.4s, 3.2s, 3.5s, and 3.1s. This problem introduces key statistical concepts like mean, variance, and standard deviation, suitable for students in Grades 9-12.

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