I have these data, representing a time series of the sales of a product:

1485, 1068, 1368, 1236, 1926, 1550, 2249,  800, 1712, 1734, 1348, 1875

The skewness of the data is -0,0512 (Excel) so I think it could be evaluated to see if the data are normally distributed. Then I made a frequency table for the data like this:

salesrange      frequency
 750 - 1000-           1
1000 - 1250-           2
1250 - 1500-           3
1500 - 1750-           3
1750 - 2000-           2
2000 - 2250-           1

So the data are approximated by bin width of 250. Plotting the frequency data I got this:


From this graph, I would say that the time series can be approximated by a normal distribution because the frequencies of their values (sales) are normally distributed (Gaussian shape).

Does this approach (check skewness and plot frequency table) make sense to say that the time series is approximately normally distributed? I know there are some normality tests but I neither know how to use them, nor am I able to because they are not part of my class program, so I'd like to know if this analysis would be acceptable.

  • $\begingroup$ Your data make no sense because (a) the table falls apart in the middle, changing from three columns to one; and (b) you haven't explained what the "range" is and it seems to have nothing to do with "sales". Please use the formatting tools available when you edit this question to clean up your table; and edit the question to include clear descriptions of what your columns mean. $\endgroup$
    – whuber
    Jun 14 '15 at 20:39
  • $\begingroup$ i'm sorry i couldn't explain it better. I hope it's clearer now $\endgroup$
    – nsp
    Jun 14 '15 at 21:14

Some cautions:

  1. Symmetry is essential for a normal distribution but an approximate bell shape is not enough to establish normality.

  2. 12 data values can sometimes rule out normality fairly convincingly; otherwise the unsurprising advice is that 12 values is a small sample to answer this question. Perhaps you have more data hidden from us.

  3. The best plot to check is arguably not a histogram but a normal quantile-quantile plot, often known as a normal probability plot. Here points would fall on a straight line if a sample were exactly normal. In this case, an informal summary of the fit is "not too bad". A serious advantage of this plot is that no arbitrary decisions are needed on binning and you show all the detail too.

enter image description here

Small print: Common recommendations are

  1. To have unambiguous bin boundaries (which bin would get 1250 if it were a value?)

  2. Never be content with Excel's lousy default of bars that don't touch when your bins do.

What software you have to hand is not really material here as software-specific questions are off-topic any way. But many readers here would advise that you can download R for free, regardless of what your institution has made available to you.

  • $\begingroup$ @NickCox Thanks for the well answered question. The purpose of this analysis is that i have to choose some time series that are qualifyed for a Reorder Point inventory replenishment that requires that the time series can be approximated to a normal distribution. I think that this instrument called Q-Q plot you introduced to me is a good test i can use for my study. I'd only have to catch up with terms like cumulative distribution factor, expected value and z-value in order to describe the process i use to plot this graph. $\endgroup$
    – nsp
    Jun 15 '15 at 9:34
  • $\begingroup$ It's "cumulative distribution function" (just to stop the wrong searches!). This plot is programmable in Excel (which you appear to be using). See e.g. youtube.com/watch?v=1Ts2lYrXenE $\endgroup$
    – Nick Cox
    Jun 15 '15 at 9:37
  • $\begingroup$ I used this video to plot the graph and the guy of the video refers to cumulative distribution factor for the cdf column. youtube.com/watch?v=U_0NY6P_xAY By the way, beside q-q plot that is good for the test, if i'd like to show also the bell shape, would it be bad to use the frequency values like i already did? $\endgroup$
    – nsp
    Jun 15 '15 at 9:46
  • 2
    $\begingroup$ Although I am not going to watch a video to check one use, I am confident that c.d. factor is not standard terminology. There is no harm in your superimposing a Gaussian density on a histogram; it's just not as good a diagnostic as a quantile-quantile plot. BTW, I didn't watch the video whose link I gave; the link was intended just as an example of stuff findable online. $\endgroup$
    – Nick Cox
    Jun 15 '15 at 10:39

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