how to find the z score

Simply take the advantages of our free handy Z-Score Calculator to calculate the z value with the help of data points or a data sample or sample mean and size easily and effortlessly. Just enter your input mean, standard deviation, data points, data sample in the input box and click on the calculate button to get the z-score value in no time.

Z-Score Calculator: Here is one of the best ways to find z-score value of your data points easily and fastly? Take the help of our online calculator tool to get the instant results by providing the mean, standard deviation and other values. This tool helps you to make your calculations faster and thus saves your precious time by giving the exact z score value in fraction of seconds along with the detailed procedure. With the explanation given, you can easily understand the concept. Check out how to find Z-Score manually in the below sections.

The following step by step procedure will help you understand the detailed explanation in solving the z-score manually. In order to find the z-score value we are having three different methods. We use those methods based on the information we are having. So, refer to the below points and get familiar with the procedure to find the z-score value

Using Data Points:

First of all, check data point, population mean, population standard deviation from the given question.
Subtract the data point from the population mean.
Divide the result by population standard deviation to get the z-score.

Using Sample Mean and Size:

Obtain sample mean, sample data size, population mean, and population standard deviation from the question carefully.
Subtract sample mean from the population mean and multiply it with the square root of data set size.
Divide the obtained value by the population standard deviation to fetch the output.

Using Data Sample:

Let us take a data sample, population standard deviation and population mean to find the z score value.
Calculate the mean for the given data sample.
Get the difference between data sample mean and population mean.
Multiply it with the square root of the data sample size.
Divide the output value by population standard deviation to find the accurate result.

Below mentioned are the formulas to calculate the z-score value in statistics.

While calculating the z score of a single data point

z = (x - μ) / σ

When calculating the z-score of a sample with known population mean and standard deviation.

z = (x_mean - μ) / σ/√n

Where, z is the z score value

x is the raw data point

x_mean is the sample data set mean

n is the sample data set size

μ is the population mean

σ is the population standard deviation

Examples

Question 1: Find the z score using data point 396, population mean and standard deviation are 400 and 20?

Solution:

Given that,

Data point x = 396

Population mean μ = 400

population standard deviation σ = 20

Z-Score formula is

z = (x - μ) / σ

Substitute values in above formula

z = (396 - 400) / 20

= -4/20

= -0.2

∴ Z-Score is -0.2

Question 2: Data sample is {12, 20, 18, 25, 33}, population mean is 50 and standard deviation is 22. Find z score value?

Solution:

Given that,

Data sample = {12, 20, 18, 25, 33}

Population mean μ = 50

population standard deviation σ = 22

Data Sample Mean x_mean = (∑_{i = 1} ⁿx_i) / n

= (12 + 20 + 18 + 25 + 33) / 5

= 108/5

= 21.6

Z-Score formula is

z = (x_mean - μ) / σ/√n

= (21.6 - 50) / 22/√5

= (-28.4 x √5) / 22

= (-28.4 x 2.23) / 22

= -63.5 / 22

= -2.88

∴ x_mean = 21.6, z-score = -2.88

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Z-Score Calculator

1. What is the z score definition?

Z score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation. The z-score is positive if the value lies above the mean, and negative if it lies below the mean.

2. What is Z score used for?

Z scores are measures of an observation's variability and can be used by traders to help determine market volatility. In z score z stands for standard score.

3. How do you use z score calculator?

You have to choose any one option from raw data point or sample mean and size or data sample. Enter data point or data sample or sample mean, data sample size, population standard deviation and mean in the specified input segments. Hit on the calculate button to get the z score value easily.

4. Find z score? When you know sample mean is 70, data sample size is 8, population mean is 59 and population standard definition is 15.

x_mean = 70, μ = 59, n = 8, σ = 15

z = (x_mean - μ) / σ/√n

= (70 - 59) / 15/√8 = (11 * √8) / 15

= 31.112/15

= 2.07