Measurements of tensile strength for 10 samples of polyethylene fibre were measured. The results are given below, in units of MPa: 2608.1 2618.5 2595.6 2589.7 2592.2 2587.3 2606.1 2623.0 2613.1 2612.5 Calculate the standard deviation of these 10 values, using the value n=10  to find the variance (use your calculator if you want to).

Give your answer to 3 significant figures. 

To calculate the standard deviation of the given 10 tensile strength measurements, we follow these steps:

1. **Calculate the mean (average) of the values.**
2. **Determine the variance using the formula:**

\[
\text{Variance} = \frac{1}{n} \sum (x_i - \bar{x})^2
\]

where:
- \( n = 10 \) (the number of samples)
- \( x_i \) are the individual measurements
- \( \bar{x} \) is the mean of the measurements

3. **Compute the standard deviation by taking the square root of the variance.**

Let's go ahead and perform these calculations.The standard deviation of the tensile strength measurements is **11.987 MPa**, rounded to three significant figures.

Would you like further details or have any questions?

Here are some related questions that might interest you:

1. How do we interpret the standard deviation in the context of material strength?
2. What is the difference between population and sample standard deviation?
3. How does variance relate to standard deviation?
4. Why is it important to use all data points when calculating standard deviation?
5. How do changes in the data set affect the standard deviation?

**Tip:** Remember that a smaller standard deviation indicates that the data points are closer to the mean, showing more consistency in the measurements.

Measurements of tensile strength for 10 samples of polyethylene fibre were measured. The results are given below, in units of MPa: 2608.1 2618.5 2595.6 2589.7 2592.2 2587.3 2606.1 2623.0 2613.1 2612.5 Calculate the standard deviation of these 10 values, using the value n=10 to find the variance (use your calculator if you want to). Give your answer to 3 significant figures.

Learn how to calculate the standard deviation of tensile strength measurements for 10 samples of polyethylene fibre, using key statistical formulas for variance and standard deviation. This step-by-step guide is suitable for students in Grades 10-12 and covers essential concepts in statistics.

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