How To Find Critical Value On Ti 84

A z-score tells u.s. how many standard deviations abroad a given value is from the hateful. The z-score of a given value is calculated equally:

z-score = (x – μ) / σ

where:

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

This tutorial explains how to summate z-scores on a TI-84 estimator.

How to Calculate the Z-Score of a Single Value

Suppose a distribution is normally distributed with a mean of 12 and a standard departure of 1.4 and we wish to calculate the z-score of an individual value ten = fourteen. To calculate the z-score in a TI-84 calculator, we would simply type 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 i.4286. In other words, the value fourteen lies one.4286 standard deviations higher up the mean.

How to Calculate the Z-Score of Several Values

Suppose instead that we take a listing of information values and that nosotros would like to calculate the z-score for every value in the list. In this case, we can perform the post-obit steps:

Step ane: Input the information.

Start, nosotros will input the data values. Press Stat and then press EDIT. Enter the following values in column L1:

Raw data values in L1 in TI-84 calculator

Step ii: Find the mean and standard deviation of the data values.

Next, we will find the hateful and the standard divergence of the dataset. PressStat and then scroll over to CALC. Highlight 1-Var Stats and pressEnter.

1-Var stats in TI-84 calculator

ForList, brand certain L1 is chosen since this is the cavalcade we entered our data in. LeaveFreqListblank. HighlightCalculateand pressEnter.

1-Var stats on TI-84 calculator

The following output will appear:

1-Var stats output on a TI-84 calculator

We tin can see that the hateful of the dataset is x = 10 and the standard deviation is s_x = 5.558. We will utilise these two values in the next step to summate z-scores.

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

Side by side, nosotros will summate the z-score for every individual value in the dataset. Printing Stat and then press EDIT. Highlight L2 and blazon in the formula (L1-10) / 5.558 and and so press Enter. The z-score of every individual value will automatically appear in column L2:

Note:To enter "L1" in the formula, printing 2d and then press 1.

Z-score calculations on a TI-84 calculator

How to Translate Z-Scores

Recall that a z-score but tells us how many standard deviations away a value is from the mean. A z-score tin be positive, negative, or equal to zero:

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

In our example, we establish that the hateful wastenand the standard deviation was5.558.

And so, the offset value in our dataset was iii, which had a z-score of (3-10) / v.558 =-1.259. This ways that the value "3" is i.259 standard deviationsbelowthe mean.

Z-score calculations on a TI-84 calculator

The side by side value in our dataset, 4, had a z-score of (4-10) / 5.558 =-1.08. This means that the value "four" is 1.08 standard deviationsbeneaththe mean.

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

For example, the value 3 is farther away from the mean compared to 4, which explains why three had a z-score with a larger absolute value.