Mean Absolute Deviation and Sampling Variability

This lesson, led by Mrs. Apia, focuses on using sample data to compare the means of two or more populations. Students learn to express differences in sample means as multiples of variability measures, specifically using the mean absolute deviation (MAD). The lesson includes practical examples, such as comparing boys' and girls' puzzle-solving times, and activities like estimating a minute with and without distractions. The goal is to understand how sample means provide evidence of population mean differences, considering sampling variability.

What is the primary focus of Lesson 22?

• Studying the effects of migraine medications

• Understanding the roles of random sampling and sampling variability

• Learning how to solve KenKen puzzles

• Exploring the use of calculators in arithmetic

What measure is used to express the difference in sample means?

• Range

• Variance

• Mean absolute deviation (MAD)

• Standard deviation

In the puzzle-solving example, what is the interval of times within one MAD for boys?

• 31.4 to 39.3 seconds

• 30.0 to 40.0 seconds

• 32.0 to 38.0 seconds

• 33.0 to 37.0 seconds

How many of the boys' sample means are within the calculated interval?

• Six

• Five

• Seven

• Four

What was the mean time for the quiet group in the estimating a minute activity?

• 58 seconds

• 61 seconds

• 59 seconds

• 60 seconds

What was the mean time for the talking group in the estimating a minute activity?

• 64.9 seconds

• 63.5 seconds

• 62.5 seconds

• 65.5 seconds

What is the MAD for the quiet group in the estimating a minute activity?

• 2.8

• 2.7

• 2.6

• 2.5

What is the MAD for the talking group in the estimating a minute activity?

• 2.5

• 2.6

• 2.7

• 2.8

How many MADs separate the means of the quiet and talking groups?

• 2.5

• 1.5

• 2.0

• 2.1

What is a key takeaway from the lesson regarding variability?

• Variability is not important in data analysis

• Variability is a natural occurrence in data distributions

• Variability should always be minimized

• Variability is only relevant for large data sets