Experimental data processing methods: comparison between table difference method and difference-by-difference method

How do the table difference method and the difference-by-difference method process experimental data respectively? What are their characteristics

Table difference method and step-by-step difference method:

1. The table difference method is to continuously calculate the difference between two adjacent rows of data in the table data, and then repeat the operation on the difference until N times of difference are equal. This method can be used to solve some numerical guessing problems.

The difference-by-difference method is a method used for data processing. Its steps are to subtract the dependent variables in the measured data one by one, or to divide the data into two groups in order and then subtract the corresponding items. The resulting differences can be treated as multiple measurements of the dependent variable. The difference-by-difference method can be used to solve some practical problems and help us analyze the changing trends and relationships of data. Through the difference-by-difference method, we can better understand the changes in the data and draw conclusions or make predictions.

【the difference】

The advantage of the table difference method is that the data is fully utilized and the formula can be fully used for calculation. However, its disadvantage is that the results are easily affected by a single data and it is relatively cumbersome to use.

The advantage of the difference-by-difference method is that it makes full use of the measurement data, can average the data, discover errors or data distribution patterns in a timely manner, and can correct or summarize the data patterns in a timely manner.

Extended information:

Commonly used data processing methods:

1. List method:

When recording and processing data, tabulate the resulting data. After the data is tabulated, the correspondence between the relevant physical quantities can be expressed in a simple, clear and compact form; it is convenient to check whether the results are reasonable at any time, find problems in a timely manner, and reduce and avoid errors; it is helpful to find out the regular connections between the relevant physical quantities , and then come up with empirical formulas, etc.

2. Drawing method:

To help process experimental data, we can use graphing to represent the relationship between two columns of data. The graphing method presents the data in the form of graphs so that the relationship between the data can be observed and analyzed more intuitively. Experimental data can be efficiently processed using mapping methods, providing additional insights and insights.

One of the methods of solving puzzles is to use model building, which can visually display the correspondence between physical quantities and reveal the connections between them when solving problems. This method is often widely used to solve various puzzles and puzzles, helping players better understand and solve problems.

Reference: Encyclopedia-Drawing Method

Encyclopedia-List Method

What is the difference-by-difference method? Conditions of Use? What are the advantages

When solving this problem, only the sum operation was used, which could not give full play to the effect of averaging multiple measurements to reduce random errors. In order to solve this problem, we can use the difference-by-difference method (difference-by-difference method) to process the data.

When using the difference-by-difference method to process data, first divide the data into two groups, and then subtract the values in the second group from the corresponding values in the first group. As shown in the following table:

n Group 1, Group 2, Difference-by-difference processing results, Uncertainty analysis

When n is an even number, each group has

Yes, both sum and sum are included, then the sum of square and root is

The following formula can be used to roughly estimate the uncertainty

When n is an odd number, we can arbitrarily discard the first data, the last data, or the middle data. However, it should be noted that if we discard a piece of data in the middle, we must consider the actual gap size between the two sets of data corresponding to the discarded data.

Example of data processing using difference-by-difference method:

In order to obtain the strength coefficient of the spring, we need to record the position to which the spring extends when the weight is lowered, and use the difference-by-difference method to calculate the average extension of the spring when a 1kg weight is added. It should be noted that this method is only applicable when the spring elongates within the elastic range, and the elongation is proportional to the external force. When measuring, we can get the actual value through estimation. The specific records and estimation results are shown in the following table: | Weight mass (kg) | Spring extension (cm) | | -------------- | --------------- | | 0 | 0 | | 1

According to the processing results of experimental data, we obtained the following data: the value of 1 is 1.00, the value of 2 is 2.00, and the value of 7.90.

2 2.00 4.01 7.92

3 3.00 6.05 7.80

4 4.00 7.95 7.87

5 5.00 9.90

6 6.00 11.93

7 7.00 13.85

8 8.00 15.82

The difference-by-difference method is a commonly used data processing method, which can improve the utilization of experimental data, reduce the impact of random errors, and reduce the instrument error component. Through the difference-by-difference method, we can process experimental data more accurately to obtain more reliable results. This makes the difference-by-difference method a commonly used analysis tool in scientific research and experiments.

Sometimes in order to appropriately increase the difference result to a period, but there is no need to output data by difference, you can continuously measure n data, leave some data unrecorded, and then record n data continuously. The difference between the two sets of data obtained can be obtained:

, the uncertainty can be estimated simply by:

The above description is about the theory of the linear difference method, which is applicable when solving the coefficient solution of a linear polynomial, provided that the independent variables change at equal intervals. In physical experiments, sometimes you may encounter quadratic difference-by-difference method and cubic difference-by-difference method to solve problems such as the coefficients of quadratic polynomials and cubic polynomials. If you want to learn more, you can refer to relevant books. Reference:

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