Find Z Score Calculator

Z-Score: 1.5.
Percentile: 93

Calculation Detail

Z = (Raw Score - Population Mean) / Standard Deviation
Z = (7 - 2.5) / 3

Tool Overview: Z Score Calculator

This Find Z Score calculator is used to convert your raw score into a standardized z score. This uses the Z score formula to automate the process of looking up this information in a z table. Enter the three factors (population mean, standard deviation, and raw score) into the calculator and it will generate the appropriate Z-Score. This standard score identifies where your raw score would fall in a standard normal distribution.

The find z score calculator will also convert your Z-score into an appropriate p-value, given in this case as percentile. This identifies the probability of seeing that raw score within a standard normal distribution, expressed as the percentage of the normal distribution under that mark. If you already have a Z-statistic and just need to calculate the p value, we have a simple p value calculator. We have another version that works for calculating the p value from a t statistic if you are working with small sample sizes and need to use Student's t-distribution.

For those of you using the find z score calculator to check statistics homework, we present a breakout of the relevant calculations. This includes both the formula and a version populated with numbers from the calculator. This is intended to help you check your calculations. It replaces a z table. If you're using R, check out the rnorm function.

FAQ - Interpreting Z Score Results

How Do You Calculate Z Score?

You can use a z score calculator (like this one) or a z score table. THe table works well with practice. You calculate your test statistic and compare it to the normal distribution curve (aka the bell curve). You may also have reference values from class.

What is Hypothesis Testing?

A rigorous way of looking at a sample and comparing it to the shape of a distribution associated with the assumption nothing is going on. We refer to this as the null hypothesis. If the data in your sample lies outside the expected range of the distribution, we will accept the alternate hypothesis - which suggests the source of your data is from a different distribution. Remember all distributions converge on the normal distribution (the normal curve) with a larger sample size due to the central limit theorem.

How Many Standard Deviation Is Significant?

Depends on the design of the test. You should set this by looking at the cost and benefit associated with being correct or incorrect. You should also remember this approach will not consider a data point unless it occurs within your sample population. If your sample population is not representative of the broader population, your inferences may not hold true. Assess the mean score (and normal score).

How is this used?

This is used both in industry and in education. A test score is intended as a representative measurement of your progress towards a binary goal: you don't know the material (null hypothesis) or do (an alternate hypothesis). We assume the results of the default state are a random variable with a visible population mean and population standard deviation. (Deviation is a measure of how much volatility to expect). The mean value is compared the curve.

Positive z score / negative z score?For a standard normal distribution, you can use the sign of the z score to assess where someone stands. A positive z score is above the mean (average) result. A negative z score is below average (median result). [for a true standard normal, the mean and median are identical).TransformationsIn some cases, you can apply another function to transform the raw value.

Speaking as a practicing analyst, concepts such as a Z-Score can be very useful when comparing the performance of similar processes measured under different conditions. For example, a larger machine might have a different level of output than a smaller machine but swings and variation in that output could certainly vary based on similar factors. This type of analysis allows you to translate these differences into a common basis and make intelligent comparisons.

Other Tools: P Value From Z Score, P Value From T Score, Confidence Interval (proportion), t critical value calculator, z critical value calculator

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