)RI ECON 261 NSC Fall 2018 Joseph Harwell &1 9/13/18 1:46A Quiz: Chapter 3 Revie

Question

)RI ECON 261 NSC Fall 2018 Joseph Harwell &1 9/13/18 1:46A Quiz: Chapter 3 Review Quiz This Question: 1 pt 7 of 22 (4 complete) This Quiz: 22 pts poss ecause the mean is very senstve to exteme values its no a resistant measure o cen er The tr mmed mean is more resistant O nd the 10% rn med mean for data set first arrange the data in order ten delete the bottom 1096 of the values and the top 10% of the values then calculate the mean of the remaining values For following dre dit rating scores, fnd a the mean, b the 10% trm med mean, ard c) the 20% t m med mean How do tre results compare? 705 788 698 557 812 764 327 778 708 713 837 742 752 a. The mean is (Round to one decimal place as needed ) b. The 10% trimmed mean Round to one decimal place as needed) How do the results compare? O A. There is zero skew in the distribution of the data because the three means are almost exactly equal O B. The distribution of the data may be skewed to the right because the mean appears to decrease slighty as values are trimmed O c. The distribution of the data may be skewed to the left because the mean appears to increase slightly as values are trimmed

Explanation / Answer

(a) Mean = 14191/20 = 709.6

(b) 10% Truncated mean :

Step 1:

Calculate g:

g = Floor(Trimmed Mean Percent X Sample Size)

= Floor(0.1 X 20)

= Floor(2)

So,

g = 2

Step 2:

Romove bottom 2 Nos. (327 & 557) and top 2 Nos. (812 & 837) from the data set.

Step 3:
Revised data set:

606,662,680,698,705,706,708,713,742,752,764,765,778,788,791,800.

10% Trimmed mean = 11658/16

                             = 728.6

(c)

20 % Trimmen mean:

Step 1:

g = Floor(0.2 X 20)

= Floor (4)

So,

g = 4

Step 2:

Remove bottom 4 Nos (327, 557, 606 & 662) and Top 4 Nos. (791, 800, 812 & 837)

Step 3:
Revised data set:

680, 698,705, 706, 708, 713, 742, 752, 764, 765, 778, 788

Step 4:

20 % Trimmed mean = 8799/12

                           = 733.3

(d)

Correct option:

C. The distribution of the data maybe skewed to the left because the mean appears to increase cslightly as values are trimmed.

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