How to Learn Intermediate Statistics for Data Science As A Self Starter[ Day - 11 ]

Intermediate Stats

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12. Standard Normal Distribution

13. Z score

14. Probability Density Function

15. Cumulative distribution function

16. Hypothesis Testing

17. Many different plotting graphs

18. Kernel Density Estimation

19. Central Limit Theorem

20. Skewness of Data

Covariance

Pearson Correlation Coefficient

Spearman Rank Correlation Coefficient

Importance of Correlation

Hypothesis Testing

Null Hypothesis

Alternative Hypothesis

Understanding Hypothesis testing

(T-test,Chi square test, p values)

12. Understanding Z-Scores in Statistics

The Z-score is a measure of how many standard deviations a data point is from the mean of the data set. It is a way to compare individual data points from different distributions or within the same distribution.

4. Applications of Z-Scores

• Standardizing Different Data Sets: Z-scores allow for the comparison of data points from different data sets with different means and standard deviations.
• Probability Calculations: In the context of a normal distribution, Z-scores can be used to determine the probability of a data point occurring within a certain range.
• Outlier Detection: Data points with Z-scores far from 0 (typically greater than 3 or less than -3) may be considered outliers.

5. Practice Problems

Try solving these problems to practice calculating Z-scores:

1. The average weight of a certain breed of dogs is 60 lbs with a standard deviation of 8 lbs. Find the Z-score for a dog that weighs 72 lbs.
2. A class has test scores with a mean of 78 and a standard deviation of 6. What is the Z-score of a student who scored 66?
3. The length of a certain type of fish is normally distributed with a mean of 15 inches and a standard deviation of 2 inches. Calculate the Z-score for a fish that is 18 inches long.