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## PSY 2007 Assignment Z-Scores Calculation

*PSY 2007 Assignment Z-Scores Calculation*

Performed the following calculations:

Determined what scores correspond to the top and bottom 10% and 25% of the data.

Transformed the z-score formula for solving for the individual score.

Determined the z-score that corresponds to the top 10% and substituted in your values for the mean and the standard deviation. Repeated the steps for the bottom 10% and the top and bottom 25%.

Determined what percentage will be between 3 and 7 for both variables.

Computed the z-score for each value. Explained the process for converting a z-score to a percentile.

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.

When the population mean and the population standard deviation are unknown, the standard score may be calculated using the sample mean (x̄) and sample standard deviation (s) as estimates of the population values.

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean.

A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.

A negative z-score reveals the raw score is below the mean average. For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.

It is useful to standardized the values (raw scores) of a normal distribution by converting them into z-scores because:

(a) it allows researchers to calculate the probability of a score occurring within a standard normal distribution;

(b) and enables us to compare two scores that are from different samples (which may have different means and standard deviations).