# How is a normal curve drawn if I have the most frequent scores, have a low frequency score, but the score is higher than most, have one of the lower scores, but have a relatively high frequency,...

How is a normal curve drawn if I have the most frequent scores, have a low frequency score, but the score is higher than most, have one of the lower scores, but have a relatively high frequency, and my score seldom occurs?

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### 1 Answer

We are asked to draw a normal curve with the following data points indicated: a score that has the largest frequency, a score with low frequency that is higher than most scores, a high frequency score that is lower than most, and a score that occurs infrequently.

(1) Recall that in a normal distribution, the mean, median, and mode are all the same and located in the center of the distribution. Thus the score with the highest frequency (the mode or modal score) is located in the geometric center of the graph.

(2) A score that is higher than most scores is located to the right of the center. The further to the right, the lower the frequency.

(3) A score lower than most is located to the left of the center, and the closer to the center the higher the frequency will be.

(4) A score with low probability (low frequency -- seldom occurs) is located far to the right/left of the center, depending on if the score is higher or lower than most scores.

For ease of demonstration, assume that you have normalized the scores. (That is, you have converted each score to its standard normal score or `z-"score" ` . Then the distribution has mean=median=mode of 0 and standard deviation of 1.)

Then the normalized score of (1) is 0. A possible score for (2) is 2, a possible score for (3) is (-1). For (4) possible scores include 3 or -3.

A possible graph:

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