Answered: The table shows the 100-meter…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The table shows the 100-meter backstroke and the 100-meter butterfly gold medal times (in seconds) for five recent competitions. Complete parts (a) and (b) below.

100 Meter Backstroke	100 Meter Butterfly
53.7	51.9
54.1	51.3
52.8	49.9
52.4	51.4
52.2	50.4

Q 1. Find and interpret (report in context) the mean and standard deviation of the gold medal times for each stroke. Select the correct interpretation of the mean for the 100-meter backstroke below and fill in the answer box within your choice. (Type an integer or decimal rounded to the nearest hundredth as needed.)

Q 2. Select the correct interpretation of the standard deviation for the 100-meter backstroke below and fill in the answer box within your choice. (Type an integer or decimal rounded to the nearest hundredth as needed.)

Q 3. Select the correct interpretation of the mean for the 100-meter butterfly below and fill in the answer box within your choice. (Type an integer or decimal rounded to the nearest hundredth as needed.)

Q 4. Select the correct interpretation of the standard deviation for the 100-meter butterfly below and fill in the answer box within your choice. (Type an integer or decimal rounded to the nearest hundredth as needed.)

Q 5 b. Compare the mean and standard deviation for the two strokes. Which stroke tends to have a faster gold medal time? Which has more variation in winning times?

The table shows the 100-meter backstroke and the 100-meter butterfly gold medal times (in seconds) for five recent competitions. Complete parts (a) and (b) below.
100-Meter Butterfly O
51.9
51.3
49.9
100-Meter Backstroke
53.7
54.1
52.8
51.4
52.4
52.2
50.4
Select the correct interpretation of the mean for the 100-meter butterfly below and fill in the answer box within your choice.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
O A. The mean gold medal time for the butterfly in the five recent competitions is
seconds
O B. The mean time for the 100-meter butterfly in the five recent competitions is
seconds.
O C. The mean gold medal time for the 100-meter butterfly in the five recent competitions is
seconds.
O D. The mean gold medal time for the 100-meter butterfly is
seconds.
Select the correct interpretation of the standard deviation for the 100-meter butterfly below and fill in the answer box within your choice.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
O A. The standard deviation for the gold medal time for the 100-meter butterfly in the five recent competitions is
seconds.
O B. The standard deviation for the gold medal time for the 100-meter butterfly is
seconds,
O C. The standard deviation for the time for the 100-meter butterfly in the five recent competitions is
seconds.
O D. The standard deviation for the gold medal time for the butterfly in the five recent competitions is
seconds.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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