Here is the transcription of the content from the worksheet:

Worksheet for Lab 1

Average Distance:

Calculations for Average Distance:

• $1.31 + 1.12 + 1.17 + 1.24 + 1.19 = 1.195$
• $2.92 + 2.78 + 2.64 + 3.26 = 2.95$
• $5.23 + 4.68 + 4.63 + 4.65 = 4.8725$
• $8.14 + 1.38 + 2.36 + 7.64 = 8.14$
• $11.98 + 10.75 + 11.25 + 10.47 = 11.1125$

Standard Deviation:

1. 0.5s → $\sigma = \sqrt{ \frac{(1.31 - 1.195)^2 + (1.12 - 1.195)^2 + (1.17 - 1.195)^2 + (1.24 - 1.195)^2 + (1.19 - 1.195)^2}{4} } = 0.837 \, \text{m}$

2. 0.75s → $\sigma = \sqrt{ \frac{(2.92 - 2.95)^2 + (2.78 - 2.95)^2 + (2.64 - 2.95)^2 + (3.26 - 2.95)^2}{4} } = 0.235 \, \text{m}$

3. 1s → $\sigma = \sqrt{ \frac{(5.23 - 4.8725)^2 + (4.68 - 4.8725)^2 + (4.63 - 4.8725)^2 + (4.65 - 4.8725)^2}{4} } = 0.239 \, \text{m}$

4. 1:25s → $\sigma = \sqrt{ \frac{(8.14 - 8.14)^2 + (7.38 - 8.14)^2 + (8.36 - 8.14)^2 + (8.68 - 8.14)^2}{4} } = 0.479 \, \text{m}$

5. 1.5s → $\sigma = \sqrt{ \frac{(11.98 - 11.1125)^2 + (10.75 - 11.1125)^2 + (11.25 - 11.1125)^2 + (10.47 - 11.1125)^2}{4} } = 0.573 \, \text{m}$

Let me know if you need further clarifications or explanations!

Would you like to dive deeper into standard deviation or average distance? Here are some related questions you might find interesting:

1. How does the standard deviation relate to the spread of data points in an experiment?
2. What is the significance of calculating the average distance in an experiment like this?
3. How does increasing the time affect the values for average distance and standard deviation?
4. Can you explain the formula for standard deviation and how it is applied in these calculations?
5. How can these results be used to analyze the precision and accuracy of the measurements?

Tip: The standard deviation gives you an idea of how spread out the values are from the mean. A smaller standard deviation means the values are closer to the average, indicating consistency in the measurements.