Questions on Mathematics

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  • Topic: Standard deviation, Dividend yield, Arithmetic mean
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  • Published : July 22, 2012
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Chapter 3 Problem 60 Page 133
Dividend yield is the annual dividend per share a company pays divided by the current market price per share expressed as a percentage. A sample of 10 large companies provided the following dividend yield data (The Wall Street Journal, January 16, 2004). Company| Yield %| Company| Yield %|

Altria Group| 5.0| General Motors| 3.7|
American Express| 0.8| JP Morgan Chase| 3.5|
Caterpillar| 1.8| McDonald’s| 1.6|
Eastman Kodak| 1.9| United Technology| 1.5|
Exxonmobil| 2.5| Wal-Mart Stores| 0.7|

a. What are the mean and median dividend yields?
Answer
1. Mean x= ∑xi / n n = 10 large companies
= (5.0 + 0.8 + 1.8 + 1.9 + 2.5 +3.7 +3.5 + 1.6 + 1.5 + 0.7) / 10 = 23 / 10
= 2.3
The Mean or average of dividend yield is 2.3 from sample of 10 large companies. 2. Median is the value in the middle when the data are arranged in ascending order. 0.7, 0.8, 1.5, 1.6, 1.8, 1.9, 2.5, 3.5, 3.7, 5.0

(1.8 + 1.9) / 2 = 1.85
The Median of dividend yield is 1.85 from sample of 10 large companies. b. What are the variance and standard deviation?
Answer
1. Variance S2 = ∑ (xi – x)2 / n-1
= [(0.7-2.3)2 + (0.8-2.3)2 + (1.5–2.3)2 + (1.6-2.3)2 + (1.8-2.3)2 + (1.9- 2.3)2 + (2.5-2.3)2 + (3.5-2.3)2 + (3.7-2.3)2 + (5.0-2.3)2] / (10-1) = (2.56 + 2.25 + 0.64 + 0.49 + 0.25 + 0.16 + 0.04 + 1.44 + 1.96 + 7.29)/(10 - 1)

= 17.08 / 9
= 1.90
The variance of dividend yield is 1.708 from sample of 10 large companies. 2. Standard deviation S = √S2
= √1.90
= 1.378
The Standard deviation is 1.378
c. Which company provides the highest dividend yield?
Answer Altria Group is the highest dividend yield which is 5.0 dividend yields. d. What is the z-score for McDonald’s ? Interpret this z-score. Answer
1. Z-scoreZi = (xi – x) / s
= (1.6 – 2.3) / 1.378...
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