Question

According to the material presented in chapter 5 of Social Statistics for a Diverse Society ed. 8, why do researchers use z scores? What are the advantages of using Z scores? Describe some research questions that would require the use of Z scores. Are there any research questions that would not be appropriate for the use of Z scores?

Answer 1

Answer :

The z-score is the institutionalized score and it discloses to us what number of standard deviations above or underneath a specific esteem is from the mean.

Assume we have an irregular variable x = 130 (math score of an understudy in the class).

Give us a chance to expect the mean of the math score is 120

with a standard deviation of 10.

Presently the z-score for the understudy's score x = 130

Z = (X - )/

=> Z = ( 130 - 120 )/ 10

=> Z = 10/10

=> Z = 1

Along these lines, the z-score of 1 implies the understudy's score x =130

is 1 standard deviation over the mean.

Researchers use z scores :-

This z-score is likewise used to discover the territory under the typical bend. To find that, we first need to decide the z-score and after that we have to utilize the standard typical table (contains pre-determined z-scores and their comparing probabilities) to locate the required likelihood.

Expectation this makes a difference!

Advantages of using Z - scores :-

• Clarity : The connection between a crude score and the dispersion of scores is much clearer.It is conceivable to get a thought of how fortunate or unfortunate a score is in respect to the whole gathering.
• Comparison: You can look at scores estimated on various scales
• Area under the bend: We know different properties of the ordinary conveyance.

By changing over to an ordinary conveyance of Z-scores, we can perceive what number of scores should fall between specific breaking points.

We can, in this manner, ascertain the likelihood of a given score happening.