# In this normal distribution of scores +1, -2, +5, and -10 what score would be the lowest, highest, and how would they be ranked in order from the lowest to the highest frequency. In addition, in a...

In this normal distribution of scores +1, -2, +5, and -10 what score would be the lowest, highest, and how would they be ranked in order from the lowest to the highest frequency. In addition, in a deviation, is a +5 always better than a deviation of -5?

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### 3 Answers

(1) We are given the scores 1,-2,5, and -10. In order from least to greatest, the scores are -10,-2,1,5.

Assuming that these are standard ` z ` scores in the normal distribution, note that negative z-scores indicate values below the mean while positive scores are above the mean. The larger the number is in absolute value, the further away from the center the value lies. The further from the center a value is located indicates lower frequency (assuming that the frequency mirrors the probability that a value occurs.)

Thus -10 has the smallest frequency (least likely to occur), 5 the second lowest, -2 the next, and 1 the largest frequency.

(In a normal distribution, values with a z-score of 1 have 84% of the scores beneath them, while a score of -10 has such a small percentage below that it is imperceptible. Only .0000001% of all scores lie above 5, etc...)

(2) Standard deviations are always positive, so I assume that you are asking about z-scores of -5 and 5. Both of these are extremely uncommon, but a negative z-score is not always bad.

For instance, you might want to be lighter than the average person of your height. You definitely would like to take fewer golf strokes than the average golfer.

When given the scores of 1, -2, 5, and -10 the numerical order, from least to greatest, would be -10, -2, 1, 5. -10 and -2 are negative numbers, meaning they are below zero. If you imagine a number line, the further you get from zero the bigger your number is, but if you are going in the negative/opposite direction, larger numbers that are negative are lower in value. With this said, a +5 is a better score than a -5.

In this normal distribution of scores +1, -2, +5, and -10 what score would be the lowest, highest, and how would they be ranked in order from the lowest to the highest frequency. In addition, in a deviation, is a +5 always better than a deviation of -5?

From lowest to highest it would be -10, -2, 1, 5

From highest to lowest it would be 5, 1, -2, -10