# 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

## 1650The z-score is .99 and the probability of less than 1650 is .8389 | ## 1220-1570The z-scores are -1.75 and .48 and the probability of between 1220 and 1570 is .6443 | ## 1380The z-score is -.73 and the probability of more than 1380 is .7673 |

## 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.