An article on pedaling techniques for endurance cyclists reported on single-leg

Question

An article on pedaling techniques for endurance cyclists reported on single-leg power at a high workload (a) Calculate the sample mean x bar and median x bar. (Round your mean to two decimal places.) x bar = x^= Interpret the sample mean and median. The median is larger than the mean, but they are still fairly close together. The mean is larger than the median, 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 251 rather than 247. Calculate the sample mean and median. (Round your mean to two decimal places.) x bar = x^= How would the mean and median change? The mean increased, and the median stayed the same. Both the mean and median decreased. Both the mean and median stayed the same. The mean decreased, and the median stayed the same. (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?

Explanation / Answer

Ans(a):
First we need to sort the given data which will be
159
172
175
180
180
182
187
187
194
200
206
210
214
247

There are total 14 data so median lies at (14/2)=7th data
from beginning 7th data = 187
from end 7th data = 187
so average of both = (187+187)/2=187
Hence Median=187
----------------------
To find mean we add given dats and divide that by 14
adding them gives 2693
so MEAN=2693/14=192.3571429

----------------
Hence Mean is larger than Median
-------------

Ans(b):
Now replace 247 by 251 and repeat the process
sorted dota will be
159
172
175
180
180
182
187
187
194
200
206
210
214
251
Median will remain same as position is not changed in sorted data
so Median=187
Adding them gives sum=2697
so Mean= 2697/14=192.6428571
so the Mean has increased and the Median stayed the same.
------------------

Ans(c):
Now remove smallest 159 and largest 251 thenrepeat the process
sorted dota will be

172
175
180
180
182
187
187
194
200
206
210
214

Median will remain same as first and last data removed so position is not changed in sorted data
Hence Median=187
Adding them gives sum=2287
now only 12 data points left
so Trimmed Mean= 2287/12=190.5833333

previous Mean was 192.6428571
so trim % is given by [(192.6428571-190.5833333)/192.6428571]*100
=[(2.0595238)/192.6428571]*100
=[0.0106908910665]*100
=1.06908910665 %

which is approx 1.07%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.