The shear strengths of 100 spot welds in a titanium alloy follow.

5408 5431 5475 5442 5376 5388 5459 5422 5416 5435
5420 5429 5401 5446 5487 5416 5382 5357 5388 5457
5407 5469 5416 5377 5454 5375 5409 5459 5445 5429
5463 5408 5481 5453 5422 5354 5421 5406 5444 5466
5399 5391 5477 5447 5329 5473 5423 5441 5412 5384
5445 5436 5454 5453 5428 5418 5465 5427 5421 5396
5381 5425 5388 5388 5378 5481 5387 5440 5482 5406
5401 5411 5399 5431 5440 5413 5406 5342 5452 5420
5458 5485 5431 5416 5431 5390 5399 5435 5387 5462
5383 5401 5407 5385 5440 5422 5448 5366 5430 5418
Round all answers to one decimal place.

Determine the shear strength that 25% of spot welds in this dataset has a higher shear strength than it.

To determine the shear strength such that 25% of the spot welds have a higher shear strength, we need to calculate the 75th percentile of the given dataset. Here's the step-by-step process:

1. **Sort the data** in increasing order.
2. **Determine the position** of the 75th percentile using the formula:

   \[
   P = \frac{75}{100} \times (n + 1)
   \]
   
   where \( n \) is the number of data points (in this case, \( n = 100 \)).

3. **Find the corresponding value** from the sorted dataset at this position or interpolate if necessary.

Let me compute the 75th percentile for you.The shear strength such that 25% of spot welds have a higher shear strength than it is approximately **5445.3**.

Would you like more details or have any further questions?

Here are 5 related questions for further practice:

1. How would you calculate the median shear strength for this dataset?
2. What is the 25th percentile (the value below which 25% of the data fall) for this dataset?
3. How does the range of shear strengths reflect the overall strength consistency of the welds?
4. How would you calculate the interquartile range (IQR) for these shear strengths?
5. How does the mean compare to the 75th percentile in this dataset?

**Tip:** The 75th percentile is often used in statistics to identify values that are relatively high in a dataset, helping to focus on the upper end of the distribution.

Determine the shear strength that 25% of spot welds in this dataset has a higher shear strength than it.

This problem focuses on calculating the 75th percentile of shear strength for 100 spot welds in a titanium alloy. Learn how to sort data, apply the percentile formula, and find the value corresponding to the 75th percentile. The calculated shear strength is approximately 5445.3. This topic covers key statistical concepts such as percentiles and data analysis, suitable for students in Grades 9-12.

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