A z-score, also known as a standard score, is a measurement that indicates how many standard deviations a data point is above or below the mean of a normal distribution. It is used to compare data points from different datasets that may have different means and standard deviations.
The steps for solving a z-score are as follows:
The z-score is important in statistics because it allows us to standardize data and make comparisons between different datasets. It also helps us identify outliers and understand how a data point relates to the rest of the dataset.
In hypothesis testing, the z-score is used to calculate the probability of obtaining a certain result if the null hypothesis is true. It is used to determine the statistical significance of a result and make decisions about whether to accept or reject the null hypothesis.
While the z-score is a useful tool in statistics, there are some limitations to its use. One limitation is that it is only applicable to data that follows a normal distribution. Additionally, the z-score may not accurately represent extreme values in a dataset, and it may not be meaningful for small sample sizes.