Practical Data Science using Python - Central Limit Theorem

The video tutorial covers the normal distribution curve, explaining how to calculate data proportions within standard deviations. It highlights the importance of understanding whether data is normally distributed and introduces tools like histograms and box plots for data visualization. The concept of percentiles is explained using box plots. The central limit theorem is discussed, emphasizing its assumptions and applications in statistics, particularly when dealing with non-normally distributed data.

What percentage of data lies between one and two standard deviations in a normal distribution?

• 34%

• 95%

• 47.5%

• 68%

Which method is NOT typically used to determine if data is normally distributed?

• Seaborn

• Histogram

• Box plot

• Scatter plot

What does the 87th percentile indicate in a data set?

• 87% of the data is above this value

• 87% of the data is below this value

• The data is skewed

• The data is normally distributed

In a box plot, what does the median represent?

• The 50th percentile

• The 75th percentile

• The 25th percentile

• The average value

What is the main purpose of the Central Limit Theorem?

• To determine percentiles

• To calculate standard deviation

• To allow statistical analysis on non-normal data

• To ensure data is normally distributed

Which of the following is NOT an assumption of the Central Limit Theorem?

• Original population must be normally distributed

• Sample size should be large

• Sample size should be greater than 30

• Sampling is done with replacement

How is the standard deviation of sample means calculated according to the Central Limit Theorem?

• By adding the population standard deviation to the sample size

• By dividing the population standard deviation by the square root of the sample size

• By multiplying the population standard deviation by the sample size

• By dividing the population standard deviation by the sample size

What is the significance of sampling with replacement in the Central Limit Theorem?

• It prevents the sample from being biased

• It allows the sample to be representative of the population

• It ensures the original population remains unchanged

• It ensures the sample size is large

Why is the Central Limit Theorem important in hypothesis testing?

• It eliminates the need for large sample sizes

• It simplifies data collection

• It allows for the use of sampling distributions

• It assumes data is normally distributed

What does the Central Limit Theorem help with when the original data is not normally distributed?

• Calculating exact data values

• Drawing inferences using sampling distribution

• Ensuring data is normally distributed

• Determining the mode of the data