Mr. Jenning's physics class built different-shaped parachutes to see which shapes were more effective. The students tested the parachutes by dropping them from a height of 25 feet and timing the fall. They calculated the summary below:


Mean = 4.2 secs	Std Dev = 0.5 sec	Min	= 2.6 secs Q1	= 3.4 secs Median	= 4.0 Secs Q3 = 5.7 secs Max = 6.8 secs


The students want to see what happens to their times when they drop the parachutes from 35 feet. They find that every drop is increased by 1.5 seconds. Find the new mean and standard deviation.
 Mean, 2.7 seconds; standard deviation, 0.5 second
 Mean, 4.2 seconds; standard deviation, 2 seconds
 Mean, 5.7 seconds; standard deviation, 0.5 second
 Mean, 4.2 seconds; standard deviation, −1 second

To find the new mean and standard deviation when every drop time is increased by 1.5 seconds, let's review the properties of the mean and standard deviation:

1. **Mean**: When a constant is added to every data point, the new mean is the original mean plus that constant.

   New mean = Original mean + 1.5 seconds  
   New mean = 4.2 seconds + 1.5 seconds  
   New mean = **5.7 seconds**

2. **Standard Deviation**: When a constant is added to every data point, the standard deviation remains unchanged because standard deviation measures how spread out the data is, and adding the same constant to every value does not affect the spread.

   New standard deviation = Original standard deviation  
   New standard deviation = **0.5 seconds**

Therefore, the correct answer is:

- **Mean = 5.7 seconds; standard deviation = 0.5 seconds.**

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:

1. How would the mean and standard deviation change if the times were multiplied by a constant instead of added?
2. What is the effect of subtracting a constant from each data point on the mean and standard deviation?
3. How do quartiles (Q1, Median, Q3) change when a constant is added to all data points?
4. If the students dropped the parachutes from 50 feet and times increased by 3 seconds, what would the new mean and standard deviation be?
5. How does the standard deviation help interpret the variability of parachute drop times?

**Tip:** When working with standard deviation, remember it only changes when the data is scaled (e.g., multiplied), not when shifted by adding/subtracting a constant.

Mr. Jenning's physics class built different-shaped parachutes to see which shapes were more effective. The students tested the parachutes by dropping them from a height of 25 feet and timing the fall. They calculated the summary below: Mean = 4.2 secs, Std Dev = 0.5 sec, Min = 2.6 secs, Q1 = 3.4 secs, Median = 4.0 secs, Q3 = 5.7 secs, Max = 6.8 secs. The students want to see what happens to their times when they drop the parachutes from 35 feet. They find that every drop is increased by 1.5 seconds. Find the new mean and standard deviation.

In this problem, students test parachutes dropped from 25 feet and calculate a mean of 4.2 seconds and a standard deviation of 0.5 seconds. They want to know how their times change when dropped from 35 feet, increasing by 1.5 seconds. Learn how to adjust the mean and standard deviation, key statistical concepts used in this problem. Suitable for Grades 9-11.

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