Question

Discuss the importance of using a normal distribution when comparing standardized test scores for students around the country who take different tests. Explain how this information can this be used by educators to make better decisions related to student learning.

150 words at least

typed paragraph form please

Answer 1

A standard score is a score that gives us a distance of the raw score with respect to a certain points(such as mean) in terms of standard deviation units. If we assume normality for the population of the scores, we may use Z-score as our choice of standardized scores.

Now Z-score(Z) measures for a normal population how many times of standard deviation() is a raw score(X) differs from the mean(), i.e.

.

Now if we assume normality for population of the test score obtained by students around the country, then using Z-score we can compare two scores that arises from different normal population with differing mean and standard deviation. So Z-score allows us to get all the scores in a same normal population with mean 0 and standard deviation 1, i.e. standard normal distribution.

From the properties of standard normal distribution, we can also say that empirically,

So using normal distribution, the standard score will most certainly lie between +3 and -3.

Using Z-score the educator can easily measure the performance of the students who take different tests. As different tests usually have different mean and standard deviations, normally two score from different tests should not be compared in the same scale.

Now a Z-score between +2 and +3 confirms that the student is better than the most. Z-score between -3 and -2 confirms that the student needs more attention as the score is deviating far from the average score of the population.

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