Mrs. Espadas' classes scored as follows on her first unit biology test:
1st period: 73 80 80 80 82 82 85 86 86 87 88 88 88 89 90
mean = 84.3 standard deviation = 4.7
8th period: 56 60 75 75 80 84 87 88 88 92 95 96 96 99 100
mean = 84.7 standard deviation =13.4
Explain why the 8th period scores produce a larger standard deviation. Describe three characteristics of students or situations that could be underlying causes of these differences in standard deviations.
Mrs. Espadas is planning lessons for her next unit in biology, which depends heavily on prerequisite skills from the first unit. What problems might arise if Mrs. Espadas planned her next unit for these two classes on the basis of their average performance, but ignored the difference in standard deviations?
What will be an ideal response?
The 8th period scores are more spread out or dispersed; on the average these scores range farther from their mean, which produces a larger standard deviation. The larger spread might be caused by individual differences in ability, amount of engaged time, motivational differences, or time of day.
Because some of the eighth period students have not learned the prerequisites for the next unit, they will have problems unless Mrs. Espadas plans some reteaching before the next unit.
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