how to find z score with mean and standard deviation
Z-Score: Definition, Calculation and Interpretation
By Dr. Saul McLeod, published 2019
What does the z-score tell you?
A z-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units. The z-score is positive if the value lies above the hateful, and negative if it lies beneath the mean.
It is too known as a standard score, because it allows comparing of scores on dissimilar kinds of variables by standardizing the distribution. A standard normal distribution (SND) is a normally shaped distribution with a mean of 0 and a standard deviation (SD) of 1 (see Fig. one).
Effigy one. A standard normal distribution (SND).
Why are z-scores important?
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 inside a standard normal distribution;(b) and enables us to compare ii scores that are from dissimilar samples (which may have unlike means and standard deviations).
How do you calculate the z-score?
The formula for calculating a z-score is is z = (ten-μ)/σ, where 10 is the raw score, μ is the population mean, and σ is the population standard deviation.
Every bit the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard departure.
Figure 2. Z-score formula in a population.
When the population mean and the population standard departure are unknown, the standard score may be calculated using the sample mean (x̄) and sample standard difference (s) every bit estimates of the population values.
How do you translate a z-score?
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 boilerplate. For example, if a z-score is equal to +i, it is ane standard departure 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 beneath the hateful.
Another way to interpret z-scores is by creating a standard normal distribution (likewise known as the z-score distribution or probability distribution).
Fig 3 illustrates the important features of any standard normal distribution (SND).
Figure three. A standard normal distribution (SND) and normal distribution.
- The SND (i.eastward. z-distribution) is ever the same shape as the raw score distribution. For example, if the distribution of raw scores if usually distributed, and so is the distribution of z-scores.
- The mean of any SND always = 0.
- The standard deviation of whatever SND always = ane. Therefore, one standard deviation of the raw score (whatever raw value this is) converts into 1 z-score unit of measurement.
The SND allows researchers to summate the probability of randomly obtaining a score from the distribution (i.e. sample). For example, there is a 68% probability of randomly selecting a score between -ane and +1 standard deviations from the mean (see Fig. 4).
Figure 4. Proportion of a standard normal distribution (SND) in percentages.
The probability of randomly selecting a score between -1.96 and +1.96 standard deviations from the mean is 95% (encounter Fig. 4). If there is less than a 5% chance of a raw score being selected randomly, then this is a statistically significant result.
Larn how to use a z-score table
How to summate a raw score when a z-score is known
Sometimes we know a z-score and desire to observe the corresponding raw score. The formula for calculating a z-score in a sample into a raw score is given below:
X = (z)(SD) + hateful
As the formula shows, the z-score and standard deviation are multiplied together, and this figure is added to the mean.
Cheque your answer makes sense: If nosotros have a negative z-score the corresponding raw score should be less than the mean, and a positive z-score must correspond to a raw score college than the mean.
How to calculate a z-score using excel
To summate the z-score of a specific value, 10, first you must calculate the mean of the sample by using the AVERAGE formula.
For example, if the range of scores in your sample begin at cell A1 and end at cell A20, the formula =Boilerplate(A1:A20) returns the average of those numbers.
Adjacent, yous mush calculate the standard deviation of the sample by using the STDEV.S formula. For example, if the range of scores in your sample begin at prison cell A1 and stop at prison cell A20, the formula = STDEV.Southward (A1:A20) returns the standard departure of those numbers.
Now to summate the z-score type the following formula in an empty cell: = (ten – mean) / [standard difference].
To brand things easier, instead of writing the mean and SD values in the formula y'all could use the prison cell values corresponding to these values. For instance, = (A12 – B1) / [C1].
Then, to calculate the probability for a SMALLER z-score, which is the probability of observing a value less than ten (the area under the curve to the LEFT of x), type the following into a bare cell: = NORMSDIST( and input the z-score you calculated).
To observe the probability of LARGER z-score, which is the probability of observing a value greater than x (the area under the curve to the Correct of x), type: =1 - NORMSDIST (and input the z-score y'all calculated).
How to reference this article:
How to reference this article:
McLeod, S. A. (2019, May 17). Z-score: definition, calculation and interpretation. Only Psychology. www.simplypsychology.org/z-score.html
Home | About The states | Privacy Policy | Advertise | Contact Us
Simply Psychology's content is for informational and educational purposes merely. Our website is not intended to exist a substitute for professional person medical advice, diagnosis, or treatment.
© Simply Scholar Ltd - All rights reserved
Source: https://www.simplypsychology.org/z-score.html#:~:text=The%20formula%20for%20calculating%20a,by%20the%20population%20standard%20deviation.
Posted by: madsensels1994.blogspot.com
0 Response to "how to find z score with mean and standard deviation"
Post a Comment