An article on pedaling techniques for elite endurance cyclis

An article on pedaling techniques for elite endurance cyclists reported on single-leg power at a high workload. 243 186 158 180 175 176 178 206 211 182 208 181 199 196 (a) Calculate the sample mean x and median z. (Round your mean to two decimal places.) x= = Interpret the sample mean and median. The mean is larger than the median, but they are still fairly close together. The median is larger than the mean, but they are still fairly close together. The median is much larger than the mean. The mean is much larger than the median. (b) Suppose that the first observation had been 254 rather than 243. Calculate the sample mean and median. (Round your mean to two decimal places.) X= X= How would the mean and median change? The mean decreased, and the median stayed the same. Both the mean and median stayed the same. The mean increased, and the median stayed the same. Both the mean and median decreased. (c) Calculate a trimmed mean by eliminating the smallest and largest sample observations. (Enter your answer to two decimal places.) What is the corresponding trimming percentage? (Round your answer to two decimal places.) (d) The article also reported values of single-leg power for a low workload. The sample mean for n = 13 observations was x = 119.8 (actually 119.7692), and the 14th observation, somewhat of an outlier, was 163. what is the value of x for the entire sample? (Round your answer to the nearest whole number.)

Solution

The sample mean is the sum of all the observations divided by the number of observations:

Xi/n

Xi is the same as X1 + X2 + X3 + … + Xn

The median is that number for which half the data is larger than it, and half the data is smaller. It is also called the 50th percentile. To calculate the median, you will first have to order the data from lowest to highest. The median is the number exactly in the middle. If the sample size, n, is even, then the median is the average of the two middle numbers.

Solving:

a)

mean = 180.07
median = 184

Interpretation: The median is larger than the mean, but they are still fairly close

b)

mean = 180.85
median = 184

Interpretation: The mean increased and the median stayed

c)

Eliminating 158 and 243

trimmed mean = 176.66

trimming percentage = 98.11

d) You are going to multiply the mean * 13 and then, you sum 163 to this value and divide it by 14.

mean = 122.85