## Practice Problems: Measures of Variability - Answer

Midterm exam scores for a small advanced neuroanatomy class are provided below. Scores represent percent of items marked correct on the exam.

 X X2 99 9801 94 8836 93 8649 88 7744 87 7569 87 7569 87 7569 75 5625 75 5625 35 1225 820 70212

## Standard Deviation

 S = 10 (70212) - 8202 10 (10-1)

S = 18.172018

## Variance

The variance is 330.22222. The standard deviation is 18.172018. The variance is the square of the standard deviation. 18.172018 squared is equal to 330.22222.

S2 = 330.22222

## Range

The range is 64. The high score is 99; the low score is 35. 99 - 35 = 64.

Range = 64

## What does this information tell you about the variability of the students' performance on the midterm?

The variability of the student's performance seems to be fairly high. Considering the traditional grading scale (60 - 69 = D, 70 - 79 = C, etc.), a standard deviation of approximately 18 seems large. It is almost the size of two letter grades.

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