Lesson 13
Standard Deviation in Real-World Contexts
- Let’s think about standard deviation in the real world.
13.1: Estimation: Marathon Runner
![Drawing of a runner at mile marker 6.](https://cms-im.s3.amazonaws.com/bpVBfvQP6SNNBpBPQG5DUUrs?response-content-disposition=inline%3B%20filename%3D%22Marathon-01%20%25281%2529.png%22%3B%20filename%2A%3DUTF-8%27%27Marathon-01%2520%25281%2529.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T011021Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=654d07c16cabbee0eac78c3c09f6304fd70c15ededa7e71e72c884f1ee3d2280)
How long will it take the runner to finish the marathon?
- Record an estimate that is:
too low about right too high - Explain your reasoning.
13.2: Calculate Standard Deviation
![A production board during movie filming](https://cms-im.s3.amazonaws.com/kFvrgEcdR9zDLbaWVfjBobsn?response-content-disposition=inline%3B%20filename%3D%22production%20board.jpg%22%3B%20filename%2A%3DUTF-8%27%27production%2520board.jpg&response-content-type=image%2Fjpeg&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T011021Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e3a2919f42427104fe1884dbfcf823c68395a8df725f8f264181cb0d2fa4c350)
Movie A ratings on a 10 point scale:
9, 8, 10, 10, 7, 1, 8, 1, 2, 8
Movie B ratings on a 10 point scale:
9, 8, 8, 7, 9, 7, 7, 9, 7, 8
Restaurant A ratings on a 100 point scale:
88, 87, 89, 90, 87, 85, 88, 91, 86, 86, 88, 89
Restaurant B ratings on a 100 point scale:
90, 65, 89, 50, 94, 93, 95, 95, 75, 70, 88, 89
- Calculate the mean and standard deviation for each data set.
- Based on these statistics, which movie and restaurant would you choose? Explain your reasoning.
13.3: Which Route is the Best Route?
Priya timed the ride from home to school on two different routes.
Here are the times in minutes:
Route A: 21.5, 23, 24, 25, 26.5
Route B: 12, 20, 24, 28, 36
- Before calculating the standard deviation, predict which route has a greater standard deviation. Explain your reasoning.
- Calculate the standard deviation and use it to decide which route you would recommend for Priya.