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Consider the following 11 observations on shear strength (MPa) of a joint bonded in a particular manner:

4.4, 16.4, 21.1, 33.1, 35.3, 36.6, 40.4, 66.5, 81.5, 90.6, 102.8

By how much could the largest observation be reduced without changing the upper fourth?

Answer :

Final answer:

The largest observation can be reduced by 12.2 MPa without changing the upper fourth.

Explanation:

To find the upper fourth, we first need to arrange the given observations in ascending order:

  1. 4.4
  2. 16.4
  3. 21.1
  4. 33.1
  5. 35.3
  6. 36.6
  7. 40.4
  8. 66.5
  9. 81.5
  10. 90.6
  11. 102.8

Next, we need to determine the value that separates the highest 25% of the data from the rest. Since we have 11 observations, the upper fourth will be the value at the 75th percentile, which is the 9th observation in this case.

The upper fourth value is 90.6 MPa.

To find the amount by which the largest observation can be reduced without changing the upper fourth, we subtract the upper fourth value from the largest observation:

Largest observation - Upper fourth value = 102.8 - 90.6 = 12.2 MPa

Therefore, the largest observation can be reduced by 12.2 MPa without changing the upper fourth.

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