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I'm looking to calculate the standard deviation when all I have is the average alongside how many records there are.

In my dataset I have been provided, I can see an average value which is reflected in the top 5 of the dataset provided.

How can I get the values in between, roughly speaking?

For example, I have an average of £735 in the top 5.

Thanks.

Chazmondo
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1 Answers1

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You can’t.

If I understand correctly, you are given the values of $n$ and $\frac1n\sum_{k=1}^nx_k$. It is not possible to recover the individual values of the $x_k$ from this, which are needed to compute the standard deviation.

MPW
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  • Thank you @MPW for the reply, am I not able to get a rough idea of the min, mid and max going by an average value and how many entries there are? – Chazmondo Jan 05 '21 at 11:47
  • Nope. Think about ${-1,1}$ vs ${-100,100}$. They both have the same average and the sam number of points, but one is clearly more widely distributed than the other. – MPW Jan 05 '21 at 11:52
  • In fact you can take any two points $x, y$ from your data set and replace them by $x+1000000$ and $y-1000000$ without changing the average or the number of points, but you will have changed the standard deviation. – MPW Jan 05 '21 at 11:55
  • Thank you @MPW, so am I able to get a rough estimate, or what other data would I need to obtain in order to get this in the first place? – Chazmondo Jan 05 '21 at 13:49
  • If you also had the average of the squared values, you could compute it – MPW Jan 05 '21 at 13:57
  • So, I have the number of enquiries a client made, alongside the average price a ticket was offered for by other merchants in the top 5 (as a single figure), would this help to get the price?

    E.g. 15 enquiries, with an average merchant price of 3423 (in the top 5 combined). @MPW

     – Chazmondo Jan 05 '21 at 14:14