A materials-testing laboratory measured the compressive strength of 10

Question

A materials-testing laboratory measured the compressive strength of 10 concrete specimens produced from the same mix. The table shows each specimen’s compressive strength and the difference between that strength and the average (arithmetic mean) strength of all 10 specimens.

After the tests were completed, one or more results may be invalidated because of testing errors. A new mean and a new standard deviation will then be calculated using only the results that remain valid.

Specimen 
 Compressive strength (MPa) 
 Difference from mean 
 
  A 
 70 
 -10 
 
  B 
 90 
 10 
 
  C 
 60 
 -20 
 
  D 
 140 
 60 
 
  E 
 105 
 25 
 
  F 
 80 
 0 
 
  G 
 115 
 35 
 
  H 
 20 
 -60 
 
  I 
 85 
 5 
 
  J 
 35 
 -45

For each of the following statements, select  True  if the statement is true based on the information provided. Otherwise, select  False .

Bunuel · Accepted Answer

Official Solution:

The mean compressive strength is 80 MPa. Standard deviation indicates how spread out the values are around the mean. Thus, a result far from the mean contributes strongly to the spread, while a result at or very close to the mean contributes little to it.

• Invalidating only specimen H would decrease the standard deviation more than invalidating only specimen G.

Look at the  Difference from mean  column and compare the absolute distances from the mean.

H is 60 MPa from the mean, while G is only 35 MPa from the mean. Removing the value farther from the mean removes more of the spread.

Therefore, invalidating H would decrease the standard deviation more than invalidating G.

Answer:  True .

• Invalidating only specimen F would increase the standard deviation.

F has a difference from the mean of 0, so its compressive strength is exactly equal to the mean.

Removing F therefore removes no deviation from the data. The mean of the remaining values stays at 80, while the same nonzero deviations are now spread across fewer observations. Thus, the standard deviation increases.

Answer:  True .

• If specimens D and H were both invalidated, the standard deviation would increase.

D and H are each 60 MPa from the mean, one above the mean and one below it. They are therefore the two most extreme values in the data.

Because they are equally far from the mean in opposite directions, removing both leaves the mean unchanged while removing the two largest deviations from it. This makes the remaining data less spread out, so the standard deviation decreases rather than increases.

Answer:  False .

Correct answer:

Statement 1: "True"
Statement 2: "True"
Statement 3: "False"

officiisnobis · Answer

True
True
False

madsb18 · Answer

True.
Imagine the bell curve of SD. if you remove the farthest point, distance from mean would decrease. Hence SD would decrease.

True. Remove the mean spacing between values would increase.

False. Farthest points removed. Distance would decrease. SD would decrease.

A materials-testing laboratory measured the compressive strength of 10

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True	False
		Invalidating only specimen H would decrease the standard deviation more than invalidating only specimen G.
		Invalidating only specimen F would increase the standard deviation.
		If specimens D and H were both invalidated, the standard deviation would increase

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A materials-testing laboratory measured the compressive strength of 10

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