I have a sample of tortillas from which I want to estimate the weighted mean (weighted according to market share) of sodium content in tortillas sold in the market. The way I collected this sample was that I looked up the market share of different brands (in percentages) and picked up samples from different top selling brands until the sum total of market share of the brands sampled became 75%. I couldn't collect the samples from all the brands due to logistic issues. Had this been an ideal case, and I had the samples from all brands, I could have easily calculated the weighted mean of tortillas.
Assuming that the sodium content in tortillas don't vary much and that I have the market share of the brands that weren't sampled, is it possible to arrive at a statistic (mean, sd, se) that can give some idea of the distribution in sodium in tortillas - similar to weighted mean but where weight percentages don't add up to 100%? I would somehow, while calculating Mean and SD/SE, like to incorporate the information that the top brands comprising of 75% of the market share were included in the sample.

Any help appreciated.

  • $\begingroup$ I'm so not a statistician, but in absence of other information, I would just adjust the weights proportionally. $\endgroup$ – tomasz Aug 8 '18 at 16:35
  • $\begingroup$ If you can pick a range of values that you are sure the sodium content of the unsampled brands lies in, you can get bounds on the value that the weighted mean of the entire market would be by choosing the minimum and then the maximum for the missing 25%. $\endgroup$ – Rahul Aug 8 '18 at 16:40

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