# Estimate required sample size in percentage of total market volume to reach representativeness

Let's assume I have a certain percentage of the total data for all spare parts sold in a country for a specific type of product (for boats or cars etc...).

I want to calculate whether I have enough information about the whole market to make meaningful statements about that market.

Edit

Thank you for your answers. I am actually unsure how to clarify my question, but I will try:

Let's start with the example given by BruceET below, i.e., the percentage of replacement headlights for Ford trucks. As the data I have is different from that type of problem, but in specific we can modify that example to be that I have a certain percentage, $$X$$ of total data about all car spare parts (i.e., Ford + Audi + ...) in a certain Country. The total market is then (Sic, cost of) $$T=$$ parts$$_{\text{Ford}}+$$ parts$$_{\text{Audi}}+\dots$$.

This includes prices and information about which part were sold (e.g., headlights, motorparts....). Now, I want to estimate my representativeness (which I guess is hard to quantify), and the margin of error for predictions I make for the unknown part $$T-X$$ of the market.

What I do not have or do not want to consider are total numbers, I just know that I have a certain percentage of the total market data and I want to start from that value.

Edit2

Let me start differently. My goal is to judge, if my sample base is significant enough to make any predictions about the total market. Let us start with a much more simple approach. In my case i am not dealing with cars, but with a very specific type of electronic spare parts.

Lets assume for now, that i only have the following information:

• The Total Marketvolume in the spare part market in one Country in Dollar (Sic, toal revenue) $$M_{total}$$
• The number $$N$$ of spare part vendors per Region $$R$$ : $$N_{R}$$
• The total sales volume of all these Vendors $$M_{vendors}$$ but not the individual volumes.
• as a Result i can calculate the "market share" by $$p=(100/M_{total})*M_{vendors}$$

What i also have is information about the ammount of parts sold for a specific group $$X_{parts,vendors}$$ from my subset of $$N_{R}$$ Vendors. For example, i do know that from these vendors 1000 x Synchronous motor TYP XYZ were sold. I do want to extrapolate the total number $$X_{parts,total}$$ of Synchronous motor TYP XYZ sold in the total market based on my kowledge of the market share of the subset of $$N_{R}$$ Vendors.

I am as a first step looking for a save and sound way to judge if my sample size is enough to make such predictions and to get a meassure of how accurate my predicton is. An if it is not enough i would like to now what type of data i need in addtion to make such judgement.

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Oct 27 at 8:02
• Maybe this: Suppose you seek the proportion $p$ of replacement headlights for Ford trucks sold in the UK and you have count $x$ sold in UK out of all $n$ sold everywhere in a particular month, then the estimate of $p$ sold in UK is $\hat p = x/n$ and a 95% confidence interval for $p$ is $\hat p \pm 1.96\sqrt{\frac{\hat p(1-\hat p)}{n}},$ where the 'margin of error' is $E=1.96\sqrt{\frac{\hat p(1-\hat p)}{n}}.$ Notice that $E$ is a function of $n,$ so you can adjust the period of info collection to make $n$ large enough to get $E$ small enough to be useful. At maximum $E = 1.96\sqrt{1/4n}.$ Oct 27 at 8:26
• Thank you for your answers! I tried to edit my question. Oct 27 at 8:50
• Percentage without counts or some other way to judge variability will be useless. If you have a stable population of approximately normally distributed dollars/pounds/euros or percentages $X_i$ over $n > 30$ (Independent) months with mean $\bar X$ and standard deviation $S,$ then an approximate 95% CI for $n,$ is $\bar X \pm 2\frac{S}{\sqrt{n}},$ where margin of error is $E =2\frac{S}{\sqrt{n}}.$ If you know or can estimate $S,$ you can see what $n$ gives useful $E.$ [Past bedtime now. Will look here later.] Oct 27 at 9:40
• @BruceET: thank you for your reply! I figured, that i would need to rephrase my question a little. While i have some of the information you hint at in your answer, i think that i need to solve a different question first. Any help would be realy appreciated. Nov 3 at 9:28