Z score is an important concept in statistics. Z score is also called standard score. This score helps to understand if a data value is greater or smaller than mean and how far away it is from the mean. More specifically, Z score tells how many standard deviations away a data point is from the mean.
Z score = (x -mean) / std. deviation
A normal distribution is shown below and it is estimated that
68% of the data points lie between +/- 1 standard deviation.
95% of the data points lie between +/- 2 standard deviation
99.7% of the data points lie between +/- 3 standard deviation
Z score and Outliers:
If the z score of a data point is more than 3, it indicates that the data point is quite different from the other data points. Such a data point can be an outlier.
For example, in a survey, it was asked how many children a person had.
Suppose the data obtained from people is
1, 2, 2, 2, 3, 1, 1, 15, 2, 2, 2, 3, 1, 1, 2
Clearly, 15 is an outlier in this dataset.
Let us use calculate the Z score using Python to find this outlier.
Step 1: Import necessary libraries
Step 2: Calculate mean, standard deviation
mean of the dataset is 2.6666666666666665 std. deviation is 3.3598941782277745
Step 3: Calculate Z score. If Z score>3, print it as an outlier.
outlier in dataset is 
Conclusion: Z score helps us identify outliers in the data.
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Improved By : nidhi_biet