This section is from the book "Cement And Concrete", by Louis Carlton Sabin. Also available from Amazon: Cement and Concrete.

The number of briquets which are made to test the strength of a given sample of cement will depend on the accuracy which it is desired to attain. If but two briquets are made, neither of the results may be rejected; however widely they may differ one from the other, the mean of the two must be considered the result of the experiment when nothing is known as to their comparative value. But if several briquets are made from the same sample, and they vary one from another, the final result is sometimes obtained by rejecting certain of the observations. In some cases if five or six specimens are made, the highest and the lowest ones are omitted, while sometimes the two lowest are rejected, and the mean of the three or four highest is taken.

221. While the absolute mean of all of the observations will ordinarily be quite sufficient, and should usually be considered the result of the test, yet where tests are very carefully made to compare two samples, or two methods of manipulation, it may be desired to reject certain observations that appear to be abnormal. The beginner in cement testing, unfamiliar with observations of this character, may not feel confidence in his own judgment as to what observations may be rejected, and the criteria sometimes used in more accurate work are entirely too complicated for this purpose. To serve as a guide in such cases, the writer would suggest the following simple method which, though entirely arbitrary, is more justifiable than either of the methods mentioned above. As the experimenter becomes more familiar with the work, he will doubtless prefer to depend on his own judgment in the rejection of observations, taking into account the general accuracy of the work.

First obtain the absolute mean and the difference between this mean and each individual result; let us call this difference the "error" for each result. Reject any observations whose error is, say, ten per cent, of the absolute mean, and obtain the mean of the remaining observations as the true result.

222. For example, suppose that we have broken ten briquets obtaining the strengths given below, and wish to determine the result of the test. The absolute mean is found to be 213.9 pounds, or, the nearest whole number, 214 pounds.

Number of Briquets. | Observed Strength. | Error. | Observed Strength. | New Error. |

1 | 209 | 5 | 209 | 1 |

2 | 226 | 12 | 226 | 16 |

3 | 227 | 13 | 227 | 17 |

4 | 184 | 30 | . . . | . . . |

5 | 217 | 3 | 217 | 7 |

6 | 252 | 38 | . . . | . . . |

7 | 200 | 14 | 200 | 10 |

8 | 195 | 19 | 195 | 15 |

9 | 193 | 21 | 193 | 17 |

10 | 236 | 22 | . . . | . . . |

Sum . . . | 2,139 | 177 | 1,467 | 83 |

Mean . . | 213.9 | 17.7 | 209.6 | 11.9 |

The "errors" are given in the third column, and it is seen that three of them are greater than ten per cent, of the mean. Omitting the results having these large errors, we obtain a new mean of 209.6 pounds, which is to be considered the result of the test. An inspection of the first column of errors shows that the mean of the errors is 17.7 pounds; if we divide this by the mean of the tensile strengths, we obtain 17.7 / 213.9 = .0827. Expressing this as a percentage, we may call 8.27 per cent, the "average error." The same result is, of course, obtained by dividing the sum of errors by the sum of the strengths. Now if we consider column five, we see that the new average error will be but 83 / 1467 = 5.66 per cent.

223. In giving the results of a series of tests, it is a common practice to state only the absolute mean, but it is of considerable interest to know the variations that occurred in breaking in order that one may judge of the reliability of the results, or, in other words, to make a rough approximation as to the probable error. For this purpose the highest and lowest result may be given, but a much better index to reliability would be to give the "average error" as explained above. However, in reporting a large number of tests, the extra labor involved in obtaining this "average error" is usually considered too great to be attempted, and in such cases the absolute mean and the highest and lowest results must serve the purpose.

When an operator has become expert and is working under good conditions, he may expect to obtain results within the following limits: The extreme variations between the results in a set of ten briquets (the difference between the highest and lowest) not exceeding 20 per cent, of the mean strength of the set, the maximum variation from the mean not exceeding 12 per cent, of the mean, and the "average error," as explained above, not exceeding 8 per cent.

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