Sampling Variability and Measures of Dispersion

The total length of the videos in this section is approximately 44 minutes, but you will also spend time answering short questions while completing this section.

You can also view all the videos in this section at the YouTube playlist linked here.

Polls

Question 1: How many people should you poll in California (population approx 38 million) to generate a sample as precise as your estimate based on 500 people from Oklahoma (population approx 3.8 million?)

It's like a bowl of soup

Question 2: Which of the following affect your ability to assess the saltiness of the soup? Check all that apply.

• whether the soup is mixed well

• whether the soup is pureed or chunky (with different pieces ending up in each spoonful

• size of spoon

• size of pot

Question 3: Which of the following affect your ability to precisely estimate the election outcome based on a poll? Check all that apply.

• whether the sample is representative

• whether the population is homogeneous (people are similar to each other)

• size of sample

• size of population

In these videos, we are using the word "precision" as a substitute for the words "uncertainty," "error," or "variance." No matter what we call it, we are discussing how much an estimate varies over different possible samples that you might draw from the population.

Question 4: When you read about an election poll, approximately how many people do you think were typically polled?

I expect that the discussion of measures of center is a review for many. Please skim that video as appropriate, but don't skip the videos on dispersion or variance, even though this is likely not your first statistics course.

Centers

Question 5: Suppose that we ask each student in a physical education class to run a mile, and we record the times. We will likely obtain a right-skewed distribution, with some students finishing the mile at about the same time as each other and some students taking much longer, with their times spread out on the right of the distribution. Which will be larger, the mean or the median mile time?

Dispersion

Question 6: If we have a right-skewed distribution, such as obtained from a class of students running a mile, will the 25th percentile or the 75th percentile be closer to the median?

• 25th closer to the median

• 75th closer to the median

• Same distance from the median

Mean/Median Absolute Deviation

Question 7: Calculate the median absolute deviation of the following values: 3,5,8

Variance, mean, and notation

Question 8: How is the variance related to the standard deviation?

• Variance = Standard Deviation

• Variance = (Standard Deviation) * (Standard Deviation)

• Variance * Variance = Standard Deviation

Question 9: What is the variance of the numbers 3, 5, and 10?

Variance and the normal distribution

Question 10: If Y follows a normal distribution with mean 10 and variance 4, 95% of values lie between two numbers. What is the lower number?

That's it!

During this tutorial you learned:

• What affects the variance of a sample estimate

• Ways to describe the center of data

• The relationship between median and mean when the distribution of the data is skewed

• Ways to describe the spread of data

• How to calculate the mean/median absolute deviation

• Definition of mean, variance, and standard deviation of a population

• The relationship between variance and standard deviation

• About a normal distribution, and how to describe it

Terms and concepts:

Center, mean, median, mode, skewed distribution, standard deviation, variance, range, min/max, quartiles/percentile, interquartile range (IQR), mean/median absolute deviation, distribution, and normal distribution