Flotation test analysis (1)

I. Overview flotation sorting is fine disseminated ores, do not choose one in particular, non-ferrous metals, rare metals, non-metallic minerals and soluble salts such as the main method. Flotation testing is an essential part of most ore selectivity studies.
(I) Contents of laboratory flotation test The main contents of the flotation test include: determining the selection scheme; determining the primary and secondary positions and mutual influences of each factor in the process by testing and analyzing the factors affecting the process, and determining The best process conditions; the final selection criteria and other necessary technical indicators. Since the selective separation of various constituent minerals during flotation is based on the difference in mineral floatability, it is the key to the flotation test to adjust the difference in mineral floatability with various agents.
(II) Procedures for laboratory flotation tests Laboratory flotation selectivity tests are usually carried out in accordance with the following procedures.
(1) Formulation of the principle plan According to the nature of the ore studied, combined with existing production experience and professional knowledge, formulate a principle plan. Metal sulfide ores such as multiple flotation, the program may have the whole principle of flotation, flotation partially mixed, flotation and other programs; red iron ore for the flotation of the possible positive flotation principle embodiment, the anti-floating Selection, flocculation and flotation.
If the principle scheme cannot be predetermined, only every possible scheme can be systematically tested to find the best one. Process conditions and indicators are finally determined by technical and economic comparisons.
(2) Preparation test conditions include sample preparation, equipment and instrument maintenance.
Objective (3) pre-test pretest is to explore the possible research programs mineral stone, and may reach the approximate range of flow principle indicators, sorting criteria.
(4) Condition test (or system test) According to the plan determined by the pre-test and the general selection conditions, a detailed test plan is prepared and systematic tests are carried out to determine the optimal flotation conditions.
(5) Closed-circuit test It is a batch test that simulates a continuous production process on a discontinuous equipment, that is, a set of laboratory closed-circuit tests in which the middle mine of the previous test is added to the corresponding location of the next test. The purpose is to determine the impact of the medium mine, verify the selected flotation conditions and processes, and determine the final indicator.
After the small-scale laboratory test, it is generally necessary to further carry out the laboratory flotation continuous test (referred to as the re-election test), and sometimes it is necessary to do semi-industrial tests or even industrial tests.
Second, flotation sample preparation, testing equipment and operating technology laboratory flotation test, usually refers to "small unit flotation test", also known as "batch flotation test." Natural ore is generally used for testing, but when exploring a new prescription, or when studying the basic theory of flotation, a pure mineral flotation test is often performed.
(1) Sample Preparation 1. Fragmentation and Separation Considering the representativeness of the sample and the efficiency of the small mill, the particle size of the flotation test is generally less than 1~3mm. The broken sample should be divided into single-sample bags for storage. The weight of each sample is 0.5~1kg, and the rare metal ore with low grade can be as much as 3kg. For the shrinkage of fine materials, a two-pointer (multi-slot divider) can be used, or a square method can be used.
2. Storage If the ore contains sulfide ore, especially if it contains a large amount of pyrrhotite, the oxidation may have a significant effect on the ore flotation test results. Therefore, the test of the sulfide ore is preferably carried out immediately after the sample is prepared. However, delays are often inevitable and measures must be taken to reduce the impact. The simple and easy way is to seal the storage under a coarser particle size (such as 6~25mm), then break the ore and prepare the sample several times, and process it in the same way every time. At the same time, it must be compared and checked. The slight difference in time and granularity has a possible impact on the test results. Stored specimens should be placed in a dry, cool, well ventilated area. Another solution is to prepare enough samples for the entire research project at a time and store them in an inert gas.
Sample contamination should be prevented during sample preparation. The incorporation of a small amount of oil will affect the normal operation of flotation, so avoid contamination of engine oil and other materials. Contamination may come from the taking and transport of the sample; or from the oil leaking from the sample processing and shrinking equipment; or from the materials and chemicals left in the equipment from the previous test. [next]
3. Grinding The cylindrical ball mills with internal wall sizes of Ñ„160*180mm and Ñ„200*200mm are commonly used in laboratories, and XMQ-67 Ñ„240*90mm cone ball mills are used for samples with a particle size of less than 1~3mm. There are smaller cylindrical barrel mills and roller grinders such as Ñ„160*160mm, which are used for regrinding of medium and fine ore products.
The grinding medium is customarily used with a ball having a diameter of 12.5 mm to 32 mm. For the Ñ„160*180mm grinding machine, the ball diameter of 25, 20, 15mm is selected. The XMQ-67 type Ñ„240*90mm cone ball mill can be equipped with a larger ball (28~32mm). The 12.5mm ball is only used for regrind operations. When a rod is used as the medium, the diameter of the rod is generally 0 to 25 mm. For example, XMB-68 type Ñ„160*200mm rod mill is often equipped with 17.5 and 20mm rods.
The effect of the amount of ball loading on the fineness of the grinding is crucial, and it is disadvantageous if it is too large or too small. The amount of ball loading is too large, the grain size of the intermediate grain size is large, and the content of the extremely coarse and very fine grain grade is small. The amount of ball loading is insufficient, not only the average grain size is coarse, but also the particle size distribution is coarse, and the particles are too large. In principle, the amount of ball loading is preferably 40 to 50% of the volume of the grinding machine, and the optimal filling rate is 45%. However, when the diameter of the grinding machine is large, the filling rate can be lower because it is often inconvenient to handle the ball. The ball mill has a high rotational speed and the filling rate should be lower.
The ratio of the balls of various sizes has little effect on the grinding grain size with respect to the filling rate and the grinding concentration. There is no certain requirement for the ratio. According to our experience, if the Ñ„160 ball mill uses three balls of 25, 20, 10mm, use q ₁ :q ₂ :q ₃ =d ⁿ ₁ :d ⁿ ₂ :d ⁿ _{3 to} indicate the weight and diameter of the three balls. Relationships, generally can be n equal to 1 ~ 3, commonly used 2, for the sake of simplicity can also take 3 (the number of balls of different sizes at this time is equal, thus easy to remember). The above ratio can ensure uniform particle size, too large particle size, but it is not easy to obtain very fine products. Therefore, the ball should be added during fine grinding. Generally, n can be equal to 0, that is, the weight of the three balls is equal. The concentration of the grinding ball should not be too high for a long time, otherwise the excessive particle size in the product will increase due to insufficient impact force. When a ball larger than 25 mm is required, the amount of the ball is generally not more than 40% of the total weight.
If the test requires avoiding iron pollution, a ceramic ball mill can be used and ceramic balls can be used as the medium, but the grinding efficiency of the ceramic grinding machine is low, so the grinding time required is long.
The grinding concentration varies with the nature of the ore, the size of the product, the type and size of the mill, and the operating habits of each research unit. Generally, the grinding concentration has a significant influence on the particle size distribution, the concentration is increased, the grinding efficiency is improved, the grinding fineness is improved, the particle size distribution is fine, and the excessively large particle size can be reduced. The concentration is high and the amount of ball is large. The ball cannot be too small, otherwise the grinding efficiency will be significantly reduced. Therefore, when using a higher concentration, it is required to fit more balls. Commonly used are 50%, 67%, 75% three concentrations, the liquid-solid ratio is 1:1, 1:2, 1:3, respectively, so the calculation of water addition is relatively simple, if other concentration values ​​are used, Calculate the amount of grinding water as follows:

100 - C
L = —————·Q
C

Where L - the amount of water to be added during grinding (L);
C—required grinding concentration (%);
Q—Ore weight (kg).
In general, when the ore is coarser and harder, a higher grinding concentration should be used. If the ore contains more mud, or the ore has a small specific gravity, or the product has a very fine particle size, a lower concentration can be used. In actual operation, if the product particle size is found to be uneven, consider increasing the concentration, but the ball should not be too small when the concentration is high. Conversely, if the product is too sticky and adheres to the wall and the ball, it is not easy to wash it down.
When the specific gravity of the sample is large or very small, the amount of grinding water can be calculated according to the solid volume accounting for 40-50% of the total volume of the slurry.
Grinding machines and media that have not been used for a long time, use quartz sand or the sample to be pre-ground to remove rust before the test. Usually, you can dry it for a while before using it, and then start the test after washing the rust. The test must be filled with lime water or clean water.
In the test, the ball of the washed rust is first put into a clean ball mill, then added with water, and finally the ore is added. It is also possible to leave a part of the water added at the end, but it is not possible to add water after adding the ore first, which will cause the ore to adhere to the end without being easily ground. When grinding, should pay attention to the normal rotation speed of the grinding machine? And accurately control the grinding time. After grinding, the slurry is poured into the ore container, the mill is tilted, and the inner wall of the mill is washed with a small bottle of water or a rubber tube connected to the faucet, and the ore is washed into the ore container. If the grinding machine such as Ñ„160*180mm does not have a ball screen, it is necessary to put a ball screen on the ore container to separate the steel ball. After the inner wall of the grinding machine is washed, lift the ball screen and shake it. Rinse the ball with a stream of fine water, until it is washed, and finally return the ball to the mill for next use. XMQ-67 type, 240*90 cone ball mill, with its own ball screen. When discharging, the cone is inclined to the discharge end, the discharge port is opened, and the slurry is placed in the ore container. Remove the feed port plug, introduce clean water, and disconnect the car and rinse. [next]
The amount of flushing water must be strictly controlled when cleaning the mill, especially when using the MXQ-67 cone ball mill. If the amount of water is too much, the flotation machine can not accommodate it. At this time, it needs to be clarified, and the excess slurry water is sucked out by a syringe or siphoned, and the slurry water is used as a supplemental water for flotation.
The laboratory uses batch open-circuit grinding, and the particle size characteristics of the grinding products are inconsistent compared with closed-circuit grinding. In the grinding circuit that is closed to the classifier, the higher specific gravity is finer than the rest of the mineral. How to reduce the above differences needs further improvement.
In order to avoid over-grinding, when the laboratory opens the mill to grind the fragile ore, the closed-circuit grinding can be used. The method is that after the raw ore is milled for a certain period of time, the product of the specified size is screened out, and the product is sifted on the sieve, and the amount of water in the grinding is added according to the weight of the product on the sieve and the grinding concentration at the time of grinding the ore. The total time of the closed-circuit grinding is equal to the time required to open the grinding mill to the specified size. For example, a polymetallic non-ferrous metal ore has been subjected to a comparative grinding test using conditions and procedures for open-circuit grinding and closed-circuit grinding. With open-circuit grinding, the content of -20μm in grinding products accounts for 47.2%, while the imitation closed-circuit grinding, -20μm only accounts for 31.6%, and the degree of mud is significantly reduced.

Figure 1 Small flotation cell

Grinding fineness is the primary factor in flotation tests. For the grinding fineness test, the flotation test must be used to determine the optimum fineness.
4. scrubbing and desliming some non-ferrous metal oxide ores, rare metal silicate ore, iron ore, phosphate ore, potassium salt, and others, may be affected ore sludge, may be performed before flotation Scrub and remove mud. The scrubbing methods are as follows: (1) stirring at a high pulp concentration (for example, 70% solids) by adding flotation hunger; (2) scrubbing with a low-speed laboratory ball mill at about 10 r/min, which is filled with metal chisel or other. Only wipe the media without grinding the ore; (3) use a rotary scrubber or other scrubbing equipment. After scrubbing, remove the slime.
The method of deliming includes: (1) deliming by elutriation. That is, adding mineral slime dispersing agent such as water glass, sodium hexametaphosphate, sodium carbonate, sodium hydroxide, etc. in grinding or scrubbing, and then pouring the slurry into a glass jar, diluting to a liquid-solid ratio of 5:1 or more, stirring and quenching After the installation, the suspended slime is removed by siphoning; (2) the flotation method is used to remove mud. That is, before flotation of useful minerals, a small amount of foaming agent is added in advance to cause most of the slime to form a foam scraping; (3) selective flocculation and desliming. After the dispersing agent is added, a flocculating agent (such as F703, humic acid, tapioca starch, polyacrylamide, etc.) with selective flocculation is added to flocculate and precipitate the useful mineral, and the slime to be removed is still dispersed in the suspension. In the slurry, the slime is then removed by siphoning. The dispersant or flocculating agent selected in the above deliming process is premised on not affecting the flotation process, and may be cleaned if necessary. A method of sanding to remove residual dispersants or flocculants that affect the flotation process.
(2) Flotation machine and flotation test operation technology
1. Flotation machine The main part of the laboratory flotation machine is an aeration stirring device and a tank body. Models and specifications are mainly determined by the difference between the two parts. Domestic models XFG flotation machine and hang XFGC trough, the XFD single-slot and multi-slot XFD-12 flotation machine, there XFDM for selecting coal flotation machine. [next]
The stirring device of the hanging tank flotation machine is a simple stirring blade mounted on the solid shaft. The air is completely sucked by the vortex formed by the slurry mixing. The amount of air sucked varies with the distance between the stirring blade and the bottom of the tank. Special attention should be paid before the test. Its distance. After the position is adjusted, the entire test should be fixed at this position. The amount of inflation of the grooved flotation machine with a large tank is often insufficient. When the ore amount is more than 500g, especially for the flotation of sulfide ore, a single tank flotation machine is often used. The slot of the hanging flotation machine is a suspended plexiglass tank with specifications ranging from a minimum of 5~35g to a maximum of 1000g.
The aeration mixing device of the single-slot flotation machine is made by simulating the existing production equipment. It consists of water wheel, cover plate, cross grid, vertical shaft, inflatable tube and other components, and has special intake valve adjustment and control. Aeration amount with automatic foaming device. The specifications are 0.5, 0.75, 1, 1.5, 3 and 8L. Except for the 8L tank, which is a fixed metal tank, the other small-sized flotation machines use suspended plexiglass tanks.
In order to improve the repeatability of test results, reduce test errors, and facilitate operation, some laboratory flotation machines with high degree of automation have been designed and manufactured at home and abroad. Such as domestic XFDC type and RC type vertical, desktop laboratory precision flotation machine, with stepless speed regulation, liquid level adjustment device, inflation adjustment device, acidity and speed digital display device, etc., has been designed to stabilize sulfide ore. Flotation machine for oxidation-reduction potential, pH value and automatic dosing device during flotation.
2. Stirring and mixing The purpose of stirring is to suspend the mineral particles, improve the effect of the agent, and make the bubbles and the ore particles reach effective contact. The slurry agitation is carried out after the agent is added to the flotation machine and before the air is fed, in order to uniformly disperse the agent and balance the action with the mineral, and the action time can be from several seconds to half an hour or longer. In the pulping process, the general flotation machine should try to avoid aeration. If a single-slot flotation machine with an inflation valve is used, the air valve should be closed; if a hanging flotation machine is used, the baffle should be lifted; if the reverse switch is used to start the flotation machine, the agitating impeller can also be reversed. turn. Sometimes it is necessary to pre-inflate the pulp without adding chemicals to expand the difference in mineral floatability, such as the separation of certain sulfide ore. The general slurry addition sequence is: pH adjuster, inhibitor or activator, collector and foaming agent.
3. Foam Control The method of generating bubbles includes a flotation machine for agitation, pressurization of air, evacuation of microbubbles from the solution, and electrolysis of the bubbles (electrolysis of water to generate oxygen and hydrogen bubbles).
According to the flotation process, the foam size, color, virtual (mineralization degree), toughness and other appearance phenomena are observed. By adjusting the amount of foaming agent, the amount of aeration, the level of the slurry, and the strict operation, the quality and scraping amount of the foam can be controlled. . The control of the volume of the foam is usually achieved by adding a foaming agent in batches. The amount of inflation is adjusted by controlling the opening of the intake valve (the distance between the impeller and the bottom of the tank) and the speed of the flotation machine. During the test, the opening size of the valve (or the distance between the impeller and the bottom of the groove) and the rotational speed should be fixed, so as to avoid introducing new variables and affecting the comparability of the test. Controlling the level of the slurry is essentially to maintain the optimum foam layer thickness. The thickness of the foam layer of the laboratory flotation machine is generally controlled at 20~50mm, so that the slurry does not overflow into the foam container. Due to the continuous scraping of the foam, the slurry level drops, and in order to ensure the continuous scraping of the foam, the water should be continuously added. If the pH of the slurry has little effect on the flotation, tap water can be added. On the contrary, it should be formulated in advance with supplemental water equal to the pH of the slurry. When manually scraping, the speed and depth of the scraping should be strictly controlled. If the operation is unstable, the test results are difficult to repeat. The foam adhering to the wall of the flotation cell must always be flushed into the tank. At the beginning and end of the foaming, the pH and temperature of the slurry must be determined and recorded. After the flotation is over, the tailings are released and the flotation machine is cleaned.
4. Water Quality affects flotation results and dosage. For example, the yellow water phthalocyanine trials done in a copper oxide ore flotation tests (test results see table below), using field tests and the production of water for domestic water, respectively experiment, when copper concentrate grade and recovery are similar, sodium sulfide The former is 1 kg more than the latter, and the difference is caused by different water quality. Therefore, attention must be paid to the composition of water in the flotation test. In the case of fatty acid collectors, the effect of water quality is mostly due to the presence of calcium and magnesium salts in the water. The content of calcium, magnesium salts, available hardness expressed. The commonly used hardness unit is Mmol/L; in the past, German hardness units (°C) were also commonly used. The millimoles of calcium and magnesium ions per liter of water correspond to 10-mg CaO and is referred to as 1 °C. When the non-sulfide ore is floated with a fatty acid collector, the hard water is softened by zeolite or ion exchange resin or the like. The general laboratory is to test the tap water in the area. After the main process conditions have been determined, it is necessary to check the production water that may be used in the future concentrator, or to make the water distribution into the future. The components that are close to each other are checked. [next]

5. Addition of the agent Before the test, the amount of the prepared drug should be sufficient for the entire test and sealed and stored in the desiccator. Before using the drug, it is necessary to understand and check the ingredients, purity, impurity content and source of the drug used to determine whether it has deteriorated.
The water-soluble agent is formulated into an aqueous solution. In order to facilitate the conversion and addition, when the weight of each ore sample is 500g, add tens to one or two hundred grams of the agent per ton of ore, which can be formulated into a concentration of 0.5%. Formulated to a concentration of 5%. When the ore amount is 1 kg, it can be formulated into 1% and 10% depending on the amount of the agent. The so-called 10% concentration means that 100g of the solution contains 10g of the drug, that is, 10g of the drug is added with 90g (corresponding to 90ml) of water, and the solution volume is not 100ml in most cases, but is between 90-100ml. . If the amount of the added drug is required to be 1 g, the amount of the added solution is not an integer, which is extremely inconvenient. Therefore, in actual dispensing, 10 g of the drug is dissolved in water to a total solution of 100 ml, that is, the actual concentration unit is "10 g / 100 ml", but it is still customarily referred to as 10%. When the concentration of the solution is very thin, the actual difference between the two is small. The amount of added drug can be calculated as follows:

qQ
V = —————
10C

Where V is the volume of the added solution (ml);
Q—unit dosage (g/t);
Q—the weight of the ore tested (kg);
C—concentration (%) of the drug.
A measuring device for adding a water-soluble agent can be a pipette, a measuring cylinder, a measuring cup or the like. When selecting a gage, an appropriate size gage must be used depending on the amount of each agent.
Non-water-soluble agents, such as oleic acid, pine oil, black medicine, etc., are added directly by syringe, but the actual weight of each drop of the drug needs to be determined in advance, and 10 or more drops of the drug can be dripped on the analytical scale. The method of measurement. If necessary, it can also be dissolved with an organic solvent such as ethanol, but the effect of the solvent on the flotation must be determined. Another method is to mix a suitable surface active compound into the medicament and stir it vigorously to emulsify it in water, for example, adding a small amount of sodium oleate to oleic acid.
A poorly water soluble agent can be added to the mill, such as lime, which can be added to the mill in solid form.
Due to decomposition, oxidation and other reasons, the prepared solution can not be left for too long, such as xanthate, sodium sulfide and the like, must be used on the same day. [next]
6. Product Processing The coarse-grained product of the flotation test can be directly filtered. If the product is very fine or contains a lot of mud, the pulp can be poured into another container first, and the coarse sand is poured first. If the filtration is still difficult, it can be directly placed on the heating plate or the drying box to evaporate; A coagulant may be added, such as adding a small amount of acid or alkali, alum, etc. to accelerate the precipitation, extracting the clear liquid and drying the product. During the drying process, the temperature should be controlled below 110 °C. If the temperature is too high, the sample will be oxidized and the result will be scrapped. For example, when the sulfide mineral is at a high temperature, S is oxidized to SO _{2 to} volatilize, resulting in a change in the sample grade. After the flotation product is dried and weighed, it must be shrunk and ground for chemical analysis. The particle size of the sample for chemical analysis should be less than 0.15mm or finer.
III. Laboratory Flotation Closed Circuit Test The closed circuit test is a batch test used to examine the effects of recycled materials. It simulates a continuous production process on discontinuous equipment. The purpose is to find out the impact of the return of the middle mine on the flotation index; adjust the amount of the chemical used in the mine ore, and check whether the slime or other harmful solids brought by the mineral ore, or whether the soluble matter will accumulate and Impede flotation; check and check the proposed flotation process to determine possible flotation indicators.
In recent years, due to the production of micro-continuous flotation devices, the laboratory flotation closed-circuit test using the batch test method will be gradually replaced by the micro-continuous flotation test, and its test index is closer to the industrial production index.
(1) Operational technology of flotation closed-circuit test The closed-circuit test is carried out in accordance with the selected procedures and conditions of the open-circuit test, and successively and repeatedly do several tests, but the intermediate products obtained each time (selected tailings, sweeping essence) The mine is modeled after the continuous production process on site, and the corresponding operation of the next test is given until the test product reaches equilibrium. For example, if a simple one-and-one-one-sweep cycle process as shown in Fig. 2 is used, the corresponding laboratory flotation closed-circuit test flow is shown in Fig. 3.

figure 2

image 3
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There is also a more complex closed-circuit test than Figure 2. In these tests, there are several selected operations. Each time the selected tailings are returned to the previous operation in general, there may be re-grinding in the middle ore.
A closed-circuit test requires two or more flotation machines, at least two people. Under normal circumstances, the closed-circuit test should be carried out 5~6 tests in succession. It is best to test whether the test product has reached equilibrium. In the process, the product (at least the concentrate) is filtered, and the filter cake is weighed or dried and weighed. If the product can be quickly tested, it is better. Whether the test is balanced is marked by whether the metal amount and yield of the last few tested flotation products are approximately equal.
If the yield of the intermediate product is increased during the test and the balance is not reached, it indicates that the middle mine has not been sorted during the flotation process, and it can only be mechanically distributed to the concentrate and tailings in the future production. Thereby the quality of the concentrate is reduced and the metal loss in the tailings is increased.
Even if the amount of minerals does not increase significantly, according to the chemical analysis results of each product, as the test progresses downwards, the grade of concentrates continues to decline, and the grade of tailings continues to rise, which has been stable, which also indicates that the mines There is no other reason, and it is necessary to study the Chinese mine separately to determine its treatment.
The following problems should be mainly paid attention to in the closed circuit test operation:
(1) With the return of intermediate products, the dosage of certain agents should be correspondingly reduced. These agents may include hydrocarbon non-polar collectors, black drugs and fatty acids, and other collectors with foaming properties, and Foaming agent.
(2) The intermediate product will bring in a large amount of water. Therefore, during the test, special attention should be paid to saving flushing water and adding water to avoid the situation that the flotation tank can not be installed. When it is necessary, the water to be released is left as flushing water. Or add water.
(3) The complexity of the closed circuit test and the possibility of product storage, requiring time delays to be minimized. The plan should be prepared in advance, and the operating procedures should be specified and strictly followed. The entire test process must be pre-engineered to mark the number of each product to avoid errors caused by confusing the label or product.
(4) The entire closed-circuit test should be done continuously to avoid the intermediate stop and the product should be put on hold for too long.
(2) Calculation method of closed-loop test results of flotation
There are three ways to calculate the final flotation index based on the results of the closed circuit test:
(1) Combine all concentrates into total concentrates, combine all tailings into total tailings, re-select the middle ore separately, re-consolidate the concentrate into the total concentrate, and then select the tailings into the total tailings. .
(2) Combine the concentrates of the last 2~3 trials after the balance is reached into the total concentrate, and the tailings are combined into the total tailings, then according to:

Total raw ore = total concentrate + total tailings
The principle reverses the indicator of total ore. The middle mines think that the in and out are equal and are calculated separately. This is similar to the method of calculating the material balance of a closed process during the design of a concentrator.
(3) Take the indicator of the last test as the final indicator.
We recommend the second method, which is now described as follows:
Assume that a total of five tests have been carried out in succession. From the third test, the weight and metal content of concentrates and tailings have been stabilized. Therefore, the results of the third, fourth and fifth tests are used as raw data for calculating the final indicators. .
Figure 3 shows the flow chart of the third, fourth and fifth tests that have reached equilibrium. The table below shows the symbols indicating the weight and grade of each product. If the three tests are regarded as one population, then the material entering the whole is entered. Have:

Raw ore 3+ ore 4+ ore 5+ medium ore 2

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