SAT Overall Scores

Not A Normal Distribution: Most Numbers Are at the ends

Overall SAT Gathered Results

1600 - 1470 - 1650 - 1550 - 1380 - 1610 - 1610 - 1570 - 1180 - 1220 - 1600 - Population Mean: 1494.55 Population Standard Deviation: 156.63

Sample Groups

Group One - 1600 - 1470 - 1220 - 1570 - mean = 1465 - Group Two - 1180 - 1600 - 1610 - 1650 - mean = 1510 - Group Three - 1610 - 1380 - 1550 - mean = 1513.33

The mean of the Sample Means = 1496.11

The mean of the sample means and the population mean are supposed to be the same thing. The calculated ones are off by roughly 2. This could be because of the wide range of data and larger numbers, but also because the groups are not entirely equal.

Standard Error and Standard Deviation

Using the formula, the standard error of the means equals 47.23. Conversely, using the calculator will get a standard deviation of 26.99. The numbers are not even close because the range of data is so broad and real applications do not always work out a nicely as problems from a book.