How to calculate the mean, median, variance, standard deviation, standard error, z-score? What do PDF and PMF mean and what is the difference? geom_point is a scatter plot? same as... How to calculate the mean, median, variance, standard deviation, standard error, z-score? What do PDF and PMF mean and what is the difference? geom_point is a scatter plot? same as point plot? Difference long/wide format. What is meant with a plot of normal PDF given? Check out parts of a box plot. When to choose mean vs median for central tendency? Difference standard error and standard deviation of the mean? What is meant with task 13? Why is the standard deviation the root of the variance? What is the sampling distribution? What is Bessel's correction and why? What is a z-score and how to calculate it? What is statistical independence? What is the confidence interval? What are factors in R? Explain the central limit theorem in simple steps. Read more

This is a summary of statistics concepts: mean, median, variance, standard deviation, standard error, PDF, PMF, scatter plot (geom_point), long/wide data formats, normal PDF, box plot, statistical independence, confidence interval, factors in R, and the central limit theorem.

Here's a summary to your questions:

1. Mean, Median, Variance, Standard Deviation, and Standard Error:

   • Mean: Sum of all data points divided by the number of points.
   • Median: Middle value of an ordered dataset.
   • Variance: Measure of data spread; average of squared differences from the mean.
   • Standard Deviation: Square root of variance, representing data spread.
   • Standard Error: Standard deviation of the sampling distribution of a statistic, typically the mean.

2. PDF and PMF:

   • PDF (Probability Density Function): Function showing the likelihood of a continuous random variable.
   • PMF (Probability Mass Function): Function showing the likelihood of a discrete random variable.

3. Scatter Plot and Point Plot:

   • geom_point in ggplot2 creates a scatter plot, which is used to depict relationships between two continuous variables.

4. Long/Wide Format:

   • Long format: Data is in a form where each row represents one time point per subject.
   • Wide format: Data from multiple time points exist in a single row.

5. Choosing Mean vs. Median:

   • Use the mean for symmetric, outlier-free data. Use the median for skewed data or outliers.

6. Standard Error vs. Standard Deviation:

   • Standard Error: Measures precision of sample mean.
   • Standard Deviation: Measures spread of data.

7. Normal PDF Plot:

   • Graphical representation of a normal distribution's probability density function.

8. Parts of a Box Plot:

   • Displays data distribution through quartiles, emphasizing median and data variability.

9. Z-score:

   • Measure of how many standard deviations a data point is from the mean. Calculated as (X - mean) / standard deviation.

10. Statistical Independence:

• Two events are independent if the occurrence of one does not affect the probability of the other.

11. Confidence Interval:

• A range of values, derived from sample data, that is likely to contain the value of an unknown population parameter.

12. Central Limit Theorem:

• The distribution of sample means approximates a normal distribution as the sample size becomes large, regardless of the population's distribution.

13. Bessel's Correction:

• Adjustment in the calculation of the sample variance; dividing by (n-1) instead of n to give an unbiased estimate of the population variance.

14. Factors in R:

• Data type used to handle categorical variables, often used in statistical modeling.

15. Sampling Distribution:

• Distribution of a statistic (like the mean) taken from multiple samples of a population.