# Mathematics and Statistics of Market Research

Here is a quick mathematical explanation for some of the statistics used in market research. As a participant in online surveys, you are included within "n", the sample size.

**Statistic** - number computed from a sample

**Parameter** - number computed using the entire population

Samples have statistics

Populations have parameters

A statistic is used to estimate a parameter's value.

n = sample size

= sample mean

u = mean of population

m = margin of error

Spread of any statistic gets narrower as "n" becomes larger. As "n" becomes larger, a statistic will inevitably be an increasingly more accurate estimate of the parameter

## The Law of Large Numbers

As the sample size increases, 's value comes closer and closer to u.

is an estimate of u

However, there is variability in our answer for , so we introduce a margin of error, "m" to be more confident in our estimate of u.

i.e. It is our belief that u is in the range of +- m

Our level of confidence is measured as a percentage. Typically we want to be 95% confident that u is +- m

To be confident we give ourselves room for error, which means a higher confidence interval.

*However, as our percentage of confidence increases, our margin of error also increases.

Ideally we want a small margin of error, but a high level of confidence.

Remember that as "n" (the sample size) increases, the spread of gets narrower. To get more accurate results, and a smaller level of error, we need to take a larger sample size (n increases). This way we have a narrow confidence interval +- m yet we are still very confident we are within the range of u.

To change m:

1. Change level of confidence (percentage of confidence increases, m increases too

2. Change the sample size (increase n, and m (margin of error) decreases.

So, to summarize, basically the more people we poll, the more accurate our result will be. When a survey is conducted, the results need to illustrate how not only the sample size feels, but how the population feels of what the sample size represents. This is where using statistics comes into play.

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