Question

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 Std Dev Min Q1 Median Q3 Max
4.2 secs 0.5 sec 2.6 secs 3.4 secs 4.0 secs 5.7 secs 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.

Answer 1

To find the new mean and standard deviation, add 1.5 seconds to the original mean and keep the standard deviation the same.

Step-by-step explanation:

Hypothesis Testing

To find the new mean and standard deviation after dropping the parachutes from 35 feet, we can use the given information and the concept of a linear transformation. The original mean was 4.2 seconds, and every drop was increased by 1.5 seconds. Adding 1.5 to each observation, we get:

New mean: 4.2 + 1.5 = 5.7 seconds
New standard deviation: Same as before, 0.5 seconds

Answer 2

Mean will increase by 1.5 sec. i.e. 5.7 sec

And, Standard deviation will remain same.

Step-by-step explanation:

Since, every drop takes 1.5 more seconds to drop. So, the Mean will increase by 1.5 sec. Example: Mean of {4, 5, 6, 7, 8} = 6

and if every observation will increase by 2 then Mean of {6, 7, 8, 9, 10} = 8.

Thus, the Mean will also increase by 2.

Also, Standard deviation measures the dispersion(scatter) of data and it is the distance from the mean. Since there is no change in distance. Thus there will be no change in standard deviation.

Further, Mean is used to measure the central tendency of data which represents the whole data in the best way. It can be found as the ratio of the sum of all the observations to the total number of observations.

Standard Deviation is the square root of the sum of square of the distance of an observation from the mean.