QUANTITATIVE ANALYSIS

Assignment 5: Quantitative Analysis

Assignment 5: Quantitative Analysis

Question 1

1.1: Less Than Cumulative Frequency Distribution

The table given below shows sales figure of iPods recorded during a Christmas festive period.

Sales

56

50

94

73

82

21

102

123

71

111

145

158

40

93

61

94

68

79

73

49

90

70

47

30

61

84

116

64

99

129

150

86

100

54

35

146

84

95

86

107

In order to make five groups of equal width, first of all range of the data is determined. From the above data, minimum and maximum figures are as follows.

Minimum = 21

Maximum = 158

Range = 158-21 = 137

Number of Classes = 5

Size of Each Class = Range / Number of Classes (Alexeyev, 2000, 44)

Size of Each Class = 137 / 5

Size of Each Class = 27.4 28

Based on the class size of 28, following class intervals are created.

Class Interval

20 - 47

48 - 75

76 - 103

104 - 131

132-159

Arranging the data into a less than cumulative frequency distribution using five groups of equal width provides following results.

Class Interval

Cumulative Frequency

Less than 19.5

0

Less than 47.5

5

Less than 75.5

17

Less than 103.5

31

Less than 131.5

36

Less than 159.5

40

1.2: Draw Graphs

1.2.1 Histogram

1.2.2 Frequency Polygon

1.2.3 “Less Than” Ogive

1.3: Ogive

1.3.1 The 65th Percentile

65th Percentile = 94

1.3.2 The Quartile Deviation

Quartile 1 = 61.00

Quartile 2 = 84.00

Quartile 3 = 101.50

Quartile 4= 158.00

Question 2

2.1: Mean and Standard Deviation for the Daily Trading Volumes

The daily trading volume for stocks traded on the New York Stock Exchange for 12 days in a certain period are listed below.

917 millions of shares

983 millions of shares

1046 millions of shares

944 millions of shares

723 millions of shares

783 millions of shares

813 millions of shares

1057 millions of shares

766 millions of shares

836 millions of shares

992 millions of shares

973 millions of shares

In order to calculate the mean of the daily trading volumes to use as estimate of population mean, following formula will be used:

Mean for the daily Trading Volumes =

Sum of all observations (total of daily trading volumes included in sample)

Number of observations of daily trading volumes

Mean for the daily Trading Volumes =

Mean for the daily Trading Volumes = 902.75 million of shares

In order to calculate the standard deviation of the daily trading volumes to use as estimate of population deviation, following formula will be used:

Standard Deviation = (Balnaves, 2007, 38)

Standard Deviation = =

Standard Deviation = = 114.18

2.2: Probability for a Particular Day to Have Trading Volumes less than 800 Million Shares

Probability that on a particular day trading volumes will be less than 800 million shares is calculated below:

Data:

Mean = 902.75

Standard Deviation = 114.18

X = 800

P (X < 800) = ?

As we know that,

Z = (X - Mean) / Standard Deviation (Ott, 2008, 84)

Z = (800 - 902.75) / 114.18

Z = -0.8999

P (X < 800) = P (Z < -0.8999)

P (Z < -0.8999) = 0.1840

Probability that on a particular day trading volumes will be less than 800 million shares is 0.1840.

2.3: Probability for a Particular Day to Have Trading Volumes will exceed 1 Billion Shares

Probability that on a particular day trading volumes will exceed 1 billion shares is calculated below:

Data:

Mean = 902.75

Standard Deviation = 114.18

X = 1 billion = 1000 million

P (X > 1000) = ?

As we know that,

Z = (X - Mean) / Standard Deviation (Balnaves, ...