![]() The density of water varies less than 1.5 mg/cm 3 over the narrow range of normal temperatures. Recall that Specific Gravity is the ratio of the density of a substance to the density of water. The calculation of the Standard Error for five samples, above, was simply to illustrate its use in excluding data points that are probably outside the set. and there was no need to calculate the Standard Error with the Sp.G. Further, we know that the pyrite elevated the value of the Sp.G. We know from examination of the crushed grains that it contained pyrite, unlike the other four samples. Should Sample #3 have been discarded? Yes. Statistically it is considered to be within the limits of probability. Since 0.12 is greater than 0.10, on statistical grounds alone, Sample #3 should not be discarded. Twice 0.062 = 0.124 = 0.12 (to 2 figures) and the difference between the Avg Sp.G. In this particular case with the values given above, the Sp.G, of Sample #3 falls just inside the limits and should not be discarded.Ĭalculating the Standard Error: 5 Samplesĭivide the sum of squares (0.0154) by 4 = 0.00385 and take its square root = 0.062. #3 + or - twice the Standard Error, then you can be 95% certain that that value is in error and can be discarded. of Sample #3 differs by more than the Sp.G. Suppose you had not thrown out Sample #3 due to the included pyrite and you calculated the Standard Error. The Standard Error of the Mean can be used in another way, too. = 4.63 + or - twice the Standard Error of the Mean. Standard Error to the rescue! You can be 95% certain that the mineral you are seeking has a Sp.G. ![]() By how much should you pad the value, both above and below to find your unknown. When you search tables or a data bank it may be unlikely that you are looking for a value of exactly 4.63. Next, divide the sum of squares by the number of samples less one (3). Row 3 is the square of the values in Row 2, followed by the sum of the squared differences. Row 2 is the difference between the Avg, Sp.G. Row 1 is a list of the Sp.G.s of the individual samples, and the Average of the group. The following is assuming we eliminated Sample 3 due to the inclusion of pyrite.Ĭalculating the Standard Error: 4 Samples Don't worry, it is not as difficult as it sounds. We are going to use a little statistics and calculate what is known as the Standard Error of the Mean. ![]() When is it legitimate to do that? Read on. The average (mean) value, 4.66, is larger than that for each of the samples, except for #3. of the individual samples in Row 4 and divide by the number of samples, 5. The best estimate of the true Specific Gravity of your unknown mineral is the average Sp.G. The Specific Gravity for minerals is customarily rounded to two decimal places. In lines 2 and 3, recall that the density of water is in g/cm 3, so numerically the mass equals the volume. The table below shows an example of the data and calculations for five samples of a mineral: The volume of the mineral sample is equal to the volume, and the mass. of each of the samples that you ran by dividing the mass in air by the volume of the mineral sample. = Density Sample/Density Water = mass of the mineral sample in air / volume of the mineral sample/ 1 g/cm 3Ĭalculate the Sp.G. This article will concentrate on the use of an electronic balance. Generally, it requires an analyst trained, and practiced, in its use, so it is rarely used by a hobbyist. It involves four weighings on an analytical balance: 1) empty, 2) containing water, 3) containing the sample, and 4) containing the sample and water. It is employed for very small specimens or grains. There is a third method, a variation on the second, that uses a small volumetric flask, called a pycnometer. But whatever the type of balance, the principles of use are the same. Balances vary widely from modern day electronic balances to chemists analytical balances, from Jolly spring scales to home shop built wooden balances. The second method employs some sort of balance to measure the mass of the mineral fragment in air and again in water. Due to the expense, the hazard (although minimal), and the specialized instruments required, this is an operation to be used only in professional laboratories. Further, a Westphal Balance, or something similar, is required to measure the resulting density of the solution. The liquids are both expensive and toxic. ![]() One uses heavy liquids that are mixed until a fragment of the unknown mineral exhibits neutral buoyancy in the solution, not sinking nor rising. There are two distinctly different methods of determining a specific gravity (Sp.G.).
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