# Mean, median, and standard deviation

1. Scores on the LSAT are approximately normally distributed. In fact, published reports indicate that approximately 40 percent of all test takers score at or between 145 and 155, and about 70 percent score at or between 140 and 160. The full range of scores is 60 pts. (120-180). Use your knowledge of normal distributions to estimate the mean, median, and the standard deviation of the LSAT.

2. Back in 1988, a smart college student thought she might want to go to law school and took the LSAT. Her score was a 42 and her percentile rank was 95. Obviously, the scoring system has changed since 1988-the scores used to be reported on a different standard scale. Back then, as you can see, a 42 was a high score; now it's not even possible to get a score that low.

Imagine that this student decides, in 2008, to apply to law school. She is considering University of Michigan Law School, which reports that the median LSAT score for the 2006 entering class is 168, and that the 25th and 75th percentiles for the class are 166 and 170, respectively.

Admission isn't based on LSAT score alone, of course, but assuming her score correlated with her grades, essays, and other admission data, do you think this student has a good chance?

To answer this question, you must first convert the 1988 LSAT score to match the current scale, using your knowledge of the normal curve and your answer to Question 1 of this exercise, and then compare it to those of the students entering UM Law School in 2006.

#### Solution Preview

1.

For the left tail of 40% percent, P value=(1-0.40)/2 = 0.30. the corresponding z value = -0.52

Mean = (145+155)/2 = 150.

Then ...

#### Solution Summary

The mean, median and standard deviations are examined.