Question

Because the mean is very sensitive to extreme​ values, it is not a resistant measure of center. The trimmed mean is more resistant. To find the​ 10% trimmed mean for a data​ set, first arrange the data in​ order, then delete the bottom​ 10% of the values and the top​ 10% of the​ values, then calculate the mean of the remaining values. For the following​ credit-rating scores, find ​(a) the​ mean, (b) the​ 10% trimmed​ mean, and​ (c) the​ 20% trimmed mean. How do the results​ compare? PLEASE SHOW WORKING.

711	709	777	805	793
788	711	679	769	608
696	832	772	332	659
564	744	789	699	755

a. The mean is 709.6.

b. what is he​ 10% trimmed mean ?

(Round to one decimal place as​ needed.)

(c) what is the​ 20% trimmed mean?

d.How do the results​ compare?

Answer 1

putting above data in ascending order:

x
332
564
608
659
679
696
699
709
711
711
744
755
769
772
777
788
789
793
805
832

b) since for 105 trimmed mean, we remove 10% of total value from top and from bottom

10% of total values =20*0.1 =2

removing top 2 values , 332,654 and bottom 2 values 805 and 832.

	x
	608
	659
	679
	696
	699
	709
	711
	711
	744
	755
	769
	772
	777
	788
	789
	793
total	11659
average	728.6875

from above 10% trimmed mean=728.6875

c)

removing 20% or 20%*20 =4 values from top and bottom:

	x
	679
	696
	699
	709
	711
	711
	744
	755
	769
	772
	777
	788
total	8810
average	734.1667

20% trimmed mean =734.1667

d)we see that trimmed mean is higher as trimmed % increases . This can be explained by the fact that data is left skewed and trimming values from both end reduces left end extreme values,.