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I am learning statistics for data analysis. I have a question regarding to compare two data sets of different standard deviation (STD). Assuming we are measuring some data on the same system with two different methods, and it gives us two different STDs (2.50 and 3.43). Without knowing much information of the system, can we tell which data is more accurate? As I am understanding from the text, STD is used to measure how data deviated from the average of measurement. But given STD=2.5 alone, can well tell if the data is scattered too much or not? Or I will as what number of STD is said to be too much for good data?

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  • $\begingroup$ Using two different measurement tools give two different STDs. $\endgroup$ – user1285419 Jan 22 '16 at 13:55
  • $\begingroup$ Standard deviation is often abbreviated SD. 'STD' is often used for something else. $\endgroup$ – BruceET Jan 22 '16 at 22:47
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If the bias is the same (there is no systematic error on the measurements), the smaller the STD, the more precise the measurement. So you can say that the ones that provide a STD of 2.5 is more accurate than the ones that provides the STD of 3.43.

Then what STD is acceptable, really depends your data (and the units that you are using). One more useful quantity to assess the quality is the STD divided by the mean. What level is acceptable really depends on the application.

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  • $\begingroup$ Thanks. So if there is bias is not the same, is that any sense to compare the different STDs? $\endgroup$ – user1285419 Jan 23 '16 at 4:16
  • $\begingroup$ Or I ask this way, if I have 1 data set only. I know the bigger STD is the more the data scatter away from mean. But how big is said to be big enough to tell that the data is not accurate? $\endgroup$ – user1285419 Jan 23 '16 at 4:26
  • $\begingroup$ I guess it's up for you to judge depending on what you intend do with the measurement. If you're doing precision mechanics, you'd probably want to be more precise than if you are doing amateur cooking. $\endgroup$ – citronrose Jan 25 '16 at 12:51

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