Summarizing Assessment Results: Understanding Basic Statistics of Score Distribution

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  • 0:05 Raw Score
  • 1:07 Normal Distribution
  • 2:17 Standard Deviation
  • 3:57 Lesson Summary
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Lesson Transcript
Instructor: Melissa Hurst
Summarizing test results is a critical component of the assessment process. In order for results to be used effectively, they must be summarized in a way that allows educators to compare the achievement of one student to others. This lesson will describe the first step in summarizing results: understanding the basic statistics of score distribution.

Summarizing Test Results: Raw Score

'My students took these tests, but now I'm being asked by the principal to summarize their test results. How am I ever going to summarize these test results? I don't even know what that means!'

You look upset. Are you having some difficulty summarizing these results? I had problems too until I learned a few methods. I can help you! I will explain what this means, why summarizing results is important and some methods you can use to summarize these test results.

The normal distribution shows the midpoint of the set of scores
Normal Distribution Midpoint

Let's start here. This test has a score of 85. This is a raw score. A raw score is the score based solely on the number of correctly answered items on the assessment. This raw score will tell you how many questions the student got right, but just the score itself won't tell you much more. Let's now move onto how scores can be used to compare one student's results to the results of other students.

Normal Distribution

All test scores fall along a normal distribution. A normal distribution is a pattern of educational characteristics or scores in which most scores lie in the middle range and only a few lie at either extreme. To put it simply, some scores will be low and some will be high, but most scores will be moderate.

The normal distribution shows two things:

  1. The variability or spread of the scores.
  2. The midpoint of the normal distribution. This midpoint is found by calculating a mean of all of the scores, or, in other words, the mathematical average of a set of scores.

For example, if we had the following raw scores from your classroom - 57, 76, 89, 92, and 95 - the variability would range from 57 being the low score to 95 being the high score. Plotting these scores along a normal distribution would show us the variability. The midpoint of the distribution is also illustrated.

Standard Deviation

The normal distribution curve helps us find the standard deviation of the scores. Standard deviation is a useful measure of variability. It measures the average deviation from the mean in standard units. Deviation, in this case, is defined as the amount an assessment score differs from a fixed value, such as the mean.

Standard deviations are used as a measure of variability
Test Score Standard Deviations

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