# why do you use x bar to express the population mean in the graph??

Can you explain why was the population mean symbolizied by x bar rather than μ in the graph???

They have used sample mean instead of population mean in the formula because it is almost impossible to get population data to determine confidence interval. It is because some data points may not be accounted for.

For example, the example given in the previous video regarding google and its ad preference prediction is based on the data it can track from its users. However, not all internet users use google services and search engine to protect their privacy. If google cannot track the habit of those users because they are using a browser that protects their user privacy, google cannot predict what ads to show those incognito users. As a result google does not have user data from the population. However, in order to monetize from the incognito users, google predicts what those users may like from its available sample data.

Hope that makes sense!

Good question, If this was a complete population instead of a sample then every data point would be known and thus the true value of the population mean would be known and certain. There for there would be no need for confidence intervals. CI's are used to give range estimates of statistics that we cannot directly measure