STAT 1031 Quiz #2 (Thu) 1. An investment you made 5 years ago has realized the following rates of return. Year Rate of Return 1 -0.15 2 -0.20 3 0.15 4 -0.08 5 0.50

Oct, 2014

(a) Compute the mean and median of the rates of return. (b) Compute the geometric mean. (c) Which one of the three statistics computed in parts(a) and (b) best describes the return over the 5-year period? Explain. (10% each) Mean = (-0.15+-0.2+0.15-0.08+0.5)/5=0.044 Median : L50=(5+1)× 100=3 ，從小排到大第三個 -0.08 Geometric mean = [(1-0.15)(1-0.2)(1+0.15)(1-0.08)(1+0.5)]0.2 – 1 = 0.0154 成長率、獲利率資料適用於幾何平均
50

2.

Find the variance and coefficient of variation.

(10% each)

18 40

54 36
1 ������−1

20 42

46 25

25 27
1 ������−1

48 33

53 28

27 40

26 45

37 25

variance : s 2 =

̅ ∑������ (������������ − ������)2 = ������=1
������ ̅ ������

̅ (∑������ ������������2 − ������������ 2 ) ������=1

coefficient of variation : CV = ̅ n=20 ，������=34.75 s2 =
1 20−1 1 20−1

× 100%

[(18 − 34.75)2 + (54 − 34.75)2 + ⋯ + (25 − 34.75)^2]=118.6184 [(18)2 + (54)2 + ⋯ + (25)2 − 20 × 34.752 ]=118.6184

或 =

CV=√118.6184 = 0.31 34.75
1

STAT 1031 Quiz #2 (Thu) 3.

Oct, 2014

A survey of subscribers to Fortune magazine asked the following question: ”How many of the last four issues have you read?” Suppose that the following frequency distribution summarizes 500 responses. Number Read 0 1 2 3 4 Total Frequency 15 10 40 85 350 500

(a) What is the mean number of issues read by a Fortune subscriber? (b) What is the standard deviation of the number of issues read?

������������
0 1 2 3 4 total
1745 500

������������
15 10 40 85 350 500

������������ ．������������
0 10 80 255 1400 1745

̅ (������������ − ������)2
12.1801 6.2001 2.2201 0.2401 0.2601

̅ ������������ (������������ − ������)2
182.7015 62.001 88.804 20.4085 91.035 444.95

Mean=

=