380 is the number given as an aim for those collecting audience surveys with Audience Finder as it will give results at a 5% margin of error at the 95% confidence level. This gives results which, if sampled well, can be relied upon to represent your audiences. This is true of any organisation no matter what size of audience they have.
Generally the larger the sample size the more accurate the data is, therefore the more accurate and robust your conclusions are about the whole audience. A sample size should be large enough that the results from the sample are applicable to the wider audience, to an appropriate degree of accuracy.
How can I go about collecting 380 responses?
Setting hourly and weekly targets helps to ensure the sample size targets are met.
The hourly targets for face-to-face interviews depends on the length of the interview process and the flow of your visitors. When setting targets for collecting email addresses it is also important to take in to account that not all visitors who volunteered their details will end up completing the survey.
A weekly target will depend on the length of your data collection period. The shorter the period, the higher the number of responses that will need to be collected per week.
For a guide on good practice for sampling, please visit: https://theaudienceagency.org/insight/good-practice-guide-to-sampling