Describe a scenario in which you explain what the raw scores are for an event or situation and then state what z score you would personally like to have for that scenario. The scenario can be grounded in reality or totally fictional. Be sure to visualize the normal distribution and the corresponding percentile ranks when deciding what a desirable z-score would be for your situation.

Make sure you convey the following in your answer:

1. The exact z score that is desirable to you (no calculations needed).
2. Why this z score is desirable to you.
3. How the measure of central tendency affects your answer.
4. How the measure of variability affects your answer.

INSTRUCTOR TIPS:

Note that the mean, or average is equivalent to a z-score of zero. By definition, the mean and a z-score of 0 are both at the 50% in a distribution. z-Scores can only be used for normally distributed interval and ratio scale datasets (that is, things measured with a number that have a normal bell-shaped curve).

• Scores that are lower than the mean have a negative z-score.
• Scores that are higher than the mean have a positive z-score.
• z-Scores are essentially the same as standard deviations.

VirtuallyALL scoresin a datasetare between:

• -3 standard deviations (that is, az-score of -3), which capturesover 49%of the scoresbelow the mean, and
• +3 standard deviations (that is, az-score of +3), which capturesover 49%of the scoresabove the mean.

The idea of central tendency deals with how well the mean, median, or mode represents a typical score. Recall that normally distributed interval and ratio data use the mean as the best measure of central tendency.

The idea of measures of variability refers to the three ways scores are compared within a dataset in terms of their relationship to each other. The three measures of variability include range, variance, and standard deviation.