Unit 7. Day 17.

The aliens take a math test. What is the point of today’s (& yesterday’s) lesson? Mars Endor Sixthgradia

65 60 70 35 90 95 85 5 85 90 80 − − − MAD: 5

Today we will practice two problems like we did yesterday

27.0 23.8 27.0 − 23.8 = 3.2 Mean MAD Air Helium Example A: 𝟐𝟓 𝟐𝟑 𝟐𝟖 𝟐𝟗 𝟐𝟕 𝟑𝟐 𝟐𝟒 𝟐𝟔 𝟐𝟐 𝟑𝟏 𝟑𝟑 𝟑𝟎 Helium 𝟏𝟗 𝟐𝟏 Mean MAD Air Helium 27.0 23.8 Calculate the difference between the sample mean distance for the football filled with air and for the one filled with helium. 27.0 − 23.8 = 3.2

Air 𝟐𝟓 𝟐𝟑 𝟐𝟖 𝟐𝟗 𝟐𝟕 𝟑𝟐 𝟐𝟒 𝟐𝟔 𝟐𝟐 𝟑𝟏 𝟑𝟑 𝟑𝟎 Helium 𝟏𝟗 𝟐𝟏 Mean MAD Air Helium 27.0 2.59 23.8 2.07 The typical deviation from the mean of 𝟐𝟕.𝟎 is about 𝟐.𝟓𝟗 𝐲𝐝. for the air−filled balls. The typical deviation from the mean of 𝟐𝟑.𝟖 is about 𝟐.𝟎𝟕 𝐲𝐝. for the helium−filled balls. There is a slight difference in variability. Calculate the MAD for each distribution. Based on the MADs, compare the variability in each distribution. Example A:

There is a separation of 𝟏. 𝟐 MADs There is a separation of 𝟏.𝟐 MADs. There is no meaningful distance between the means. Mean MAD Air Helium 27.0 2.59 2.59 23.8 2.07 Based on your calculations, is the difference in mean distance meaningful? Difference of the means: 27.0−23.8 = 3.2 3.2 𝑣𝑠. Example A:

Example B: College 𝟒𝟏 𝟔𝟕 𝟓𝟑 𝟒𝟖 𝟒𝟓 𝟔𝟎 𝟓𝟗 𝟓𝟓 𝟓𝟐 𝟓𝟎 𝟒𝟒 𝟒𝟗 H.S. 𝟐𝟑 𝟑𝟑 𝟑𝟔 𝟐𝟗 𝟐𝟓 𝟒𝟑 𝟒𝟐 𝟑𝟖 𝟐𝟕 𝟑𝟓 Mean MAD College High School 52,400 (or 52.4) 32,800 (or 32.8) Calculate the difference between the sample mean salary for college graduates and for high school graduates.. 52,400 − 32,800 = 19,600

5.15 5.17 Mean MAD College 52,400 High School 32,800 𝟒𝟏 𝟔𝟕 𝟓𝟑 𝟒𝟖 𝟒𝟓 𝟔𝟎 𝟓𝟗 𝟓𝟓 𝟓𝟐 𝟓𝟎 𝟒𝟒 𝟒𝟗 H.S. 𝟐𝟑 𝟑𝟑 𝟑𝟔 𝟐𝟗 𝟐𝟓 𝟒𝟑 𝟒𝟐 𝟑𝟖 𝟐𝟕 𝟑𝟓 Mean MAD College 52,400 High School 32,800 5.15 5.17 The typical deviation from the mean of 𝟓𝟐.𝟒 is about 𝟓.𝟏𝟓 (or $𝟓,𝟏𝟓𝟎) for college graduates. The typical deviation from the mean of 𝟑𝟐.𝟖 is about 𝟓.𝟏𝟕 ($𝟓,𝟏𝟕𝟎) for high school graduates. The variability in the two distributions is nearly the same. Calculate the MAD for each distribution. Based on the MADs, compare the variability in each distribution. Example A:

Difference of the means: 52.4−32.8 = 19.6 19.6 There is a separation of 𝟑.𝟕𝟗 MADs. There is a meaningful difference between the population means. Mean MAD College 52,400 5.15 High School 32,800 5.17 5.17 Based on your calculations, is the difference in mean distance meaningful? Difference of the means: 52.4−32.8 = 19.6 19.6 𝑣𝑠. Example B:

Conclusion NO “meaningful difference” between sample means A difference in between two sample means is considered “meaningful” when the difference is at least twice as large as the MAD. NO “meaningful difference” between sample means YES “meaningful difference” between sample means