Reconstructing dataset given mean, median and Stdev

In summary, the speaker is asking if it is possible to reconstruct a dataset given the mean, median, standard deviation, and N of the dataset. They provide an example where there are 20 students in a class with a mean exam score of 80, median of 85, standard deviation of 14, and one student with a score of 96. They also mention that there are 20 variables and only a few equations, making it difficult to find an exact solution.
  • #1
ruberhelios
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Wondering if it is possible to reconstruct a dataset if I give you the mean, median, standard deviation and N of a dataset.

For example, if there are 20 students in a class. The mean of their exam score is 80, median is 85, standard deviation is 14. Of course the maximum score for the exam can only be 100 and minimum zero. I can also further tell you that one student got 96.

Is there a way to reconstruct an approximate dataset to reflect these conditions? Thanks for your attention!
 
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  • #2
In the abstract you have 20 variables and only a few equations, so there are many possible solutions.
 

1. How do I reconstruct a dataset given the mean, median, and standard deviation?

To reconstruct a dataset given the mean, median, and standard deviation, you can use the following formula: dataset = mean + (median - mean) * (dataset - mean) / stdev. This formula will help you calculate the values for each data point in the dataset.

2. Can I reconstruct a dataset if I only have the mean and standard deviation?

Yes, you can reconstruct a dataset if you only have the mean and standard deviation. However, the dataset will not be unique, as there are infinite combinations of data points that can give the same mean and standard deviation. In this case, it is recommended to also have the median to reconstruct a more accurate dataset.

3. What assumptions are necessary to successfully reconstruct a dataset using mean, median, and standard deviation?

The main assumption necessary to successfully reconstruct a dataset using mean, median, and standard deviation is that the dataset follows a normal distribution. This means that the data is symmetric and bell-shaped, with the mean, median, and mode all at the center of the distribution.

4. Are there any limitations to using mean, median, and standard deviation to reconstruct a dataset?

Yes, there are limitations to using mean, median, and standard deviation to reconstruct a dataset. These measures only provide information about the central tendency and spread of the data, and do not take into account the individual data points or their distribution. Additionally, as mentioned before, the reconstructed dataset may not be unique and may not accurately represent the original dataset.

5. Is there a more accurate method for reconstructing a dataset compared to using mean, median, and standard deviation?

Yes, there are other methods for reconstructing a dataset that may be more accurate than using mean, median, and standard deviation. These methods include using quartiles and percentiles, as well as fitting a specific statistical distribution to the data. These methods take into account the individual data points and their distribution, providing a more accurate reconstruction of the dataset.

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