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What is a Z Table used for in Statistics?

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What is a Z Table: Overview

The z-table is short for the Standard Normal Z-Table. The Standard Normal distribution is used in hypothesis testing, including tests on proportions and on the difference between two means. The area under the whole of a normal curve is 1, or 100 percent. The z-table helps by telling us what percentage is under the curve at any particular point.

What is a Z Table: Standard Normal Probability

Every set of data has a different set of values. For example, heights of people might range from eighteen inches to eight feet and weights can range from one pound (for a preemie) to five hundred pounds or more. Those wide ranges make it difficult to analyze data, so we “standardize” the normal curve, setting it to have a mean of zero and a standard deviation of one. When the curve is standardized, we can use a Z Table to find percentages under the curve.

Percentages under the curve

what is a z table used for

This graph shows the standardized normal graph with the percentage of results (data) that will fall between standard deviations on that graph. For example, 68.27 percent of results will fall within one standard deviation of the mean. On this graph, it’s represented by two z-scores from the z table: the area between z=-1 and z=1.

The z-table

Obviously a graph can only give us so much information. The above graph can tell us the area under the curve for one (z= -1 to 1), two (z= -2 to 2) and three (z= -3 to 3) standard deviations from the mean. But what about if we want to know the area between z=-0.78 and z=0.78? Or z=-1.2 and z=0.44? That’s where the z-table comes in. It tells us the area under the standard normal curve for any value between the mean, zero and any z-value.

Why Are There Two z-tables?

Simply, it’s to make life easier. Sometimes you’ll want to know the area between the mean (0) and some positive value. That’s when you’ll use the regular z-table (area to the right of z). But other times you might want to know the area in a left tail. If that’s the case, use the z-table that shows the area to the left of z.

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