FREQUENCY DISTRIBUTION & GRAPHIC PRESENTATION ( EX. # 32 & 30 )
SUBMITTED TO:
FARZANA LALARUKH DEPT. OF FINANCE UNIVERSITY OF DHAKA
SUBMITTED BY:
SHEAKH MOHAMMAD KHALED MAHTAB ID# 11046 DEPT. OF FINANCE EMBA UNIVERSITY OF DHAKA
Date of submission: February 27, 2007
Exercise # 32 The Midland National Bank selected a sample of 40 student checking accounts. Below are their endofthemonth balances:
404 87 703 968
74 234 125 712
234 68 350 503
149 489 440 489
279 57 37 327
215 185 252 608
123 141 27 358
55 758 521 425
43 72 302 303
321 863 127 203
a) Tally the data into a frequency distribution using $100 as a class interval and $0 as the starting point. b) Draw a cumulative frequency polygon. c) The bank considers any student with an ending balance of $400 or more a "preferred customer." Estimate the percentage of preferred customers. d) The bank is also considering a service charge to the lowest 10% of the ending balances. What would you recommend as the cutoff point between those who have to pay a service charge and those who do not?
Exercise # 30 The number of shareholders for a selected group of large companies (in thousands) is: Company Southwest Airlines General Public Utilities Occidental petroleum Middle South Utilities Daimler Chrysler Stander oil California Bethlehem Steel Long Island Lighting RCA Greyhound Corporation Pacific Gas & Electric Niagara Mohawk Power E. I. du Pont de Nemours Westinghouse Electric Union Carbide BankAmerica Northeast Utilities Number of share holders(thousands) 144 177 266 133 209 264 160 143 246 151 239 204 204 195 176 175 200 Company Stander Oil(Indiana) Home Depot Detroit Edison Eastman Kodak Dow Chemical Pennsylvania power American Electric power Ohio Edison Transamerica Corporation Columbia Gas System International Telephone & Telegraph Union Electric Virginia Electric & power Public Service Electric &Gas
Number of share holders(thousands) 173 195 220 251 137 150 262 158 162 165 223 158 162 225 161
Consumers Power
The numbers of shareholders are to be organized into a frequency distribution & several graphs drawn to portray the distribution. a) b) c) d) Using seven classes and a lower limit of 130, construct a FD. Portray the distribution as a frequency polygon Portray the distribution in a cumulative frequency polygon. According to the polygon, 3 out of 4 (75%) of the companies have how many share holders or less?
e) Wright a brief analysis of the number of shareholders based on the FD & graphs.
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Solution # 32 Below are the endofmonth balances of The Midland National Bank selected 40 student checking accounts. 404 87 703 968 74 234 125 712 234 68 350 503 149 489 440 489 279 57 37 327 215 185 252 608 123 141 27 358 55 758 521 425 43 72 302 303 321 863 127 203
(a) Number of observation,N = Highest Value, H.V. = Lowest Value, L.V. = Number of Classes (K) => Class Interval (i) i ≥ => i ≥ 2 k k
40 968 27
≥ =
40 10
H.V.  L.V. K 968 27 10 100
=>
i=
SL.No.
Class Interval 0 100 200 300 400 500 600 700 800 900 1000
Frequency
1 2 3 4 5 6 7 8 9 10
0 100 200 300 400 500 600 700 800 900 Total=

9 6 6 6 5 2 1 3 1 1 40
Cumulative Frequency 0 9 15 21 27 32 34 35 38 39 40
b) To draw cumulative distribution table, we scale the upper limit of each class along the Xaxis and the corresponding cumulative frequency along the Yaxis. To provide additional information, we label the vertical axis on the left from 0 to 40 units and the vertical axis on the right from 0 to 100 percent. To begin the plotting, 9 students has the endofmonth balances for less than $100, so the first plot is at X=100 and Y=9, the coordinate of the next plot are X=200 and Y=15. The rest of the points are plotted and then the dots connected to form the chart.
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Cumulative frequency polygon
Y
800, 38
Number of students
30
400, 27
500, 32
80 70 60
25...