200-Meter Run The table show the gold medal Olympic times (in seconds) for the 200-meter run. Data are shown for the first five Olympics of the 1900s and five more recent Olympics in the 2000s. (Source: World Almanac and Book of Facts 2017) a. Find and interpret (report in context) the mean and standard deviation of the winning times for the first five Olympics of the 1900s. Round to the nearest hundredth of a second. b. Find the mean and standard deviation of the winning times for the more recent Olympics. c. Compare the winning times of the early 1900s and the 2000s Olympics. Are recent winners faster or slower than those of the early 1900s? Which group has less variation in its winning times?
200-Meter Run The table show the gold medal Olympic times (in seconds) for the 200-meter run. Data are shown for the first five Olympics of the 1900s and five more recent Olympics in the 2000s. (Source: World Almanac and Book of Facts 2017) a. Find and interpret (report in context) the mean and standard deviation of the winning times for the first five Olympics of the 1900s. Round to the nearest hundredth of a second. b. Find the mean and standard deviation of the winning times for the more recent Olympics. c. Compare the winning times of the early 1900s and the 2000s Olympics. Are recent winners faster or slower than those of the early 1900s? Which group has less variation in its winning times?
200-Meter Run The table show the gold medal Olympic times (in seconds) for the 200-meter run. Data are shown for the first five Olympics of the 1900s and five more recent Olympics in the 2000s. (Source: World Almanac and Book of Facts 2017)
a. Find and interpret (report in context) the mean and standard deviation of the winning times for the first five Olympics of the 1900s. Round to the nearest hundredth of a second.
b. Find the mean and standard deviation of the winning times for the more recent Olympics.
c. Compare the winning times of the early 1900s and the 2000s Olympics. Are recent winners faster or slower than those of the early 1900s? Which group has less variation in its winning times?
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 + ...
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.