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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:
- (P) This is the percentile ranking or probability of lesser values in a normal distribution. It has a range from 0.0 to 1.0
- (μ) This is the mean of the normal distribution.
- (σ) This is the standard deviation of the normal distribution.
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.
- What is the cut off score for going on the field trip?
- P is 95% (0.95), mu is 72 and sd is 13. Using this calculator, what is the answer?
- What is the cut off score for having the writing assignment?
- P is 5% (0.05), mu is 72 and sd is 13. Using this calculator, what is the answer?
RELATED CALCULATORS:
- To compute the percentile of a single observation (y) in a set (X), CLICK HERE.
- To sort a list of numeric values, CLICK HERE.
- To create a random subset of the a list of numeric values, CLICK HERE.
The Math
The formula for the z SCORE is as follows:
zy= y-μXs 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.
