How To Find Z Score Ti 84

A z-score tells united states of america how many standard deviations away a given value is from the mean. The z-score of a given value is calculated as:

z-score = (10 – μ) / σ

where:

x: individual value
μ: population mean
σ: population standard deviation

This tutorial explains how to calculate z-scores on a TI-84 calculator.

How to Calculate the Z-Score of a Single Value

Suppose a distribution is unremarkably distributed with a hateful of 12 and a standard divergence of 1.4 and we wish to summate the z-score of an private value x = 14. To calculate the z-score in a TI-84 reckoner, nosotros would simply blazon in the following formula:

Z-score calculation on a TI-84 calculator

This tells us that an individual value of 14 has a z-score of 1.4286. In other words, the value fourteen lies one.4286 standard deviations above the hateful.

How to Calculate the Z-Score of Several Values

Suppose instead that nosotros take a list of data values and that we would similar to calculate the z-score for every value in the list. In this case, we can perform the following steps:

Pace 1: Input the information.

Offset, we will input the data values. Printing Stat and and so press EDIT. Enter the following values in cavalcade L1:

Raw data values in L1 in TI-84 calculator

Step 2: Find the mean and standard difference of the data values.

Side by side, we will find the mean and the standard deviation of the dataset. PressStat and then roll over to CALC. Highlight 1-Var Stats and printingEnter.

1-Var stats in TI-84 calculator

ForList, make sure L1 is called since this is the cavalcade we entered our information in. Get outFreqListblank. HighlightCalculateand pressEnter.

1-Var stats on TI-84 calculator

The following output will appear:

1-Var stats output on a TI-84 calculator

We can meet that the mean of the dataset is x = x and the standard departure is s_x = 5.558. We will use these 2 values in the next step to calculate z-scores.

Step 3: Use a formula to calculate every z-score.

Side by side, we will summate the z-score for every individual value in the dataset. Press Stat and so press EDIT. Highlight L2 and type in the formula (L1-ten) / 5.558 and then press Enter. The z-score of every individual value volition automatically announced in cavalcade L2:

Note:To enter "L1" in the formula, press 2nd and and so press i.

Z-score calculations on a TI-84 calculator

How to Interpret Z-Scores

Recall that a z-score simply tells united states of america how many standard deviations away a value is from the hateful. A z-score tin can be positive, negative, or equal to naught:

A positive z-score indicates that a particular value is greater than the hateful.
A negative z-score indicates that a particular value is less than the mean.
A z-score of aught indicates that a particular value is equal to the mean.

In our case, we plant that the hateful wasxand the standard divergence was5.558.

So, the first value in our dataset was 3, which had a z-score of (3-x) / v.558 =-1.259. This means that the value "3" is ane.259 standard deviationsbelowthe hateful.

Z-score calculations on a TI-84 calculator

The next value in our dataset, 4, had a z-score of (4-x) / 5.558 =-1.08. This means that the value "4" is ane.08 standard deviationsbelowthe mean.

The further away a value is from the mean, the higher the accented value of the z-score volition be for that value.

For instance, the value iii is farther away from the hateful compared to 4, which explains why iii had a z-score with a larger absolute value.