The raw score from the Percentile, Mean and Standard Deviation calculator computes the raw score (y) associated with a percentile rank (P) in a normal distribution with a mean (μ) and standard deviation (σ).
INSTRUCTIONS: Enter the following:
Raw Score: The calculator returns the raw score associated with the percentile ranking in the normal distribution. This raw score calculator is also a prominent feature with other statistical functions in the College Level Statistics Calculator (Stat Calc).
Example: A teacher says that the students with final exam grades in the top 5% of her class will go on a special field trip, and that the lowest 5% will have to write "I will study harder" a thousand times. If the final exam test scores are normally distributed with a mean of 72 and a standard deviation of 13.
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The formula for the z SCORE is as follows:
`z_y = (y - μ_X)/s` where:
- y is the single observation
- μ is the mean
- s is the sample or population standard deviation.
If we solve for y, the formula is as follows:
y = z * s + mu
Therefor we use the percentile ranking (P) to look up the z SCORE and compute the value of y.