Lesson 2.2 - Transforming Data Quick Notes Lesson App 2.2 How fast does light travel? Light travels fast, but it is not transmitted instantly. Light takes over a second to reach us from the moon and over 12 billion years to reach us from the most distant objects in the universe. Because radio waves and radar also travel at the speed of light, having an accurate value for that speed is important in communicating with astronauts and satellites in orbit. An accurate value for the speed of light is also important to computer designers because electrical signals travel at light speed. The first reason- ably accurate measurements of the speed of light were made between July and September 1882 by A. A. Michelson and Simon Newcomb. Newcomb made 66 measurements of the time in seconds that a light signal took to pass from his laboratory on the Potomac River to a mirror at the base of the Washington Monument and back, a total distance of about 7400 meters. Newcomb's first measurement of the passage time of light was 0.000024828 second, or 24,828 nano- seconds. (There are 109 = 1billion nanoseconds in a second.) To keep the numbers manageable, we converted them to deviations from 24,800 nanoseconds. So Newcomb's first measurement is recorded as 28. The minimum value of -44 corresponds to a measurement of 24,756 nanoseconds. The following figure provides a histogram and numerical summaries for these data. Suppose we convert the passage time measurements to nanoseconds by adding 24,800 to each value. 1. What shape would the resulting distribution have? but It 25 20 Frequency 5 15 2. Find the median of the distribution in nanoseconds. 10 -45 -30 -15 0 15 30 45 3. Find the /QR of the distribution in nanoseconds. Passage time (deviations from 24,800 nanoseconds) " Mean SD Min Q, Med Q, Max 66 26.21 1075 -44 24 27 31 After performing the transformation to nanoseconds, we could convert the measurements from nanoseconds to seconds by dividing each value by 109. 4. Describe the shape, center (median), and variability (/QR) of this distribution. d variability 5. Challenge: Use the information provided to estimate the speed of light in meters per second. Be prepared to explain the method you used. STATS M