# Standard Score: Definition & Examples

## Introduction

The standard score is a part of the standard deviation and it is a datum or observation. The score has many similarities with the standard deviation and they are compared easily. The datum that is in the upper position of the mean is the representation of the standard score in a positive way. The lower position of the datum of the mean indicates the score in a negative way.

## What is a Standard Score?

The standard score determines the distance between the standard deviation’s score and the unit mean. The score is also called standardised variables, Z score, normal score and many more. The Z score calculates the gap between the population and raw score. The standard deviations represent the populations and the raw score in the unit. The test of IQ is the perfect example to understand the standard score. Mean is a unit of the score and its score is average rather than other unit scores. The score helps to define the particular number between mean or (M or $\mathrm{\mu}$) and the score of standard deviations or (s or $\mathrm{\sigma}$). Raw score mean and standard deviations are needed to calculate the standard score.

## Standard Score: Characteristics

Many important characteristics are available in standard score like, the score can be utilised in the score distribution process for comparison. The mean, standard deviations, raw materials come out from the distribution procedure. The score is mostly used for score comparison in a proper way. The second characteristic of the score is that bigger deviations are created from a bigger standard score. The unit mean contains the further raw score and bigger standard score.

The score decreased to zero is a sign that the score stayed on the mean unit. Another characteristic defines that the gap between the score and it mean in the standard deviations is called as standard score. The score can be in a negative state or in a positive state and if z score is positive then the score will be bigger than the mean. The score will be lesser than Mean at the time of Z score in a negative state.

The significance of Z score is cannot be determined by the negative or positive signs. An example, +1.0 is smaller than the -2.0 Z score. Z=+1 has a smaller distance with the unit mean but Z = -2.0 has a double distance with the unit mean. The negative or positive signs of the Z score determine the score distance from the unit mean. The exact value of the Z score determines the magnitude of the standard score.

## Standard Score: Formula

The standard score calculating formula is described below,

$$\mathrm{Z=X-\mu/\sigma}$$

The above formula described that the score (X) is subtracted by the unit mean and makes a division between them. Z represents the standard score and the calculation happens in normal distribution with raw score. The standard deviation of one class is S = 1 and the standard deviation of another class is S = 5. The score of S = 1 based class will be X = 80 and S = 5 based class’s score will be X = 85. The mean or the average score of both classes will be seventy-five and eighty. The equation looks like, Z = 80 - 75/1 = 5 and another class’s standard score is Z = 85 - 80/5 = 1. The score can be utilized for comparing two classes' performances. The scoring standard (Z) is converted from the score (X) during the time of distribution of the score.

## Applications of Standard Score

The help of calculating standard score one must gain knowledge about the relationship between standard deviation and the unit mean. The applications of the scores are described below,

• The score is helped to make students analogues and it is the most popular standardised method. Sometimes the task of calculating the total population looks very harder but with the help of a standard score, it becomes easier.

• The lower endpoint and upper endpoint are the two intervals of prediction for determining the Standard Score. The observation of the future population gives an indication of these two intervals.

• The procedure’s off-target is operated by process constant.

A few advantages of using the standard score are described below,

• The score helps to determine the value of raw data from the unit mean in the standard deviation unit. Assume that the standard score of two means the value of standard deviation is also two.

• The score is very useful in the time of comparison between two data. The score helps to calculate the relative value and probability in the normal standard distribution.

A few disadvantages of using a standard score are described below,

• The standard score cannot resolve the ordinal or nominal types of data.

• The score cannot recover the original values of data. The values can be recovered with the help of standard deviations and distributions.

## Conclusion

The standard score determines the distance between the score of standard deviations and the unit mean. The score’s definition and the examples are the main discussable topic of the above article. The characteristics of the standard score and the difference between the Z score and the standard score are also described in this tutorial along with the applications, advantages and disadvantages.

## FAQs

Q1. How many types of standard scores can be found in statistics?

Ans. There are about 4 types of standard scores that can be applied to analyse data and extract results from it. The four standard scores are Percentiles, IQ scores, T scores and Z scores.

Q2. What are the concepts of average in the standard score?

Ans. The standard score can generate three distinctive types of average when analysing a dataset. The first type of average is the low average that has a limit between 80 and 89. The second type of average is the standard average that has a range 90 to 109. The final type of average is high average with a value 110 to 119.

Q3. What is the right way to determine the standard score from specific data?

Ans. The process of extracting the standard score from specific data follows the pathway of subtracting the mean from the dataset. For example, if 28 is subtracted with 24, the result will be 4. Therefore, the difference between the mean and the standard deviation here will result as a standard score of 0.8.

Updated on: 06-Jan-2023

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