How to find point estimate mean and SD

Question

The National Football League (NFL) polls fans to develop a rating for each football game (NFL website, October 24, 2012). Each game is rated on a scale from  (forgettable) to  (memorable). The fan ratings for a random sample of  games follow.

Excel File: data07-11.xlsx

a. Develop a point estimate of mean fan rating for the population of NFL games.

 

b. Develop a point estimate of the standard deviation for the population of NFL games (to 4 decimals).

 

Answer 1

Hi Lourdes,

a. To get point-estimate for the mean, simply add all ratings and divide by 12, the number of games in the sample. Sample means are typically denoted as "x-bar." Thus:

x-bar=(57+61+86+74+72+73+20+57+80+79+83+74)/12

x-bar=68

b. Standard deviation is a bit more complicated. We are working with a point-estimate i.e. a sample; sample standard deviation is typically denoted "s." The formula:

s=sqrt(sum(x_i-x-bar)²/n)

I will break this down:

sum=add total of all differences

x_i=individual observation--eg. x₁=57, x₂=61, etc.

x-bar=sample mean=68

n=sample size=12

Now, ideally we shouldn't have to do those calculations manually--we can use statistical software or a graphing calculator, but this is just so you understand what those tools are doing and just in case an instructor requires this to be done manually. From a calculator:

s=17.89

Keep in mind that this measure is likely inflated by the one fan who rated 20! I hope this helps.