Question

The commercial banking industry is undergoing rapid changes due to advances in technology and competitive pressures in the financial services sector. The data file BANKS contains selected information tabulated by Fortune concerning the revenues, profitability, and number of employees for the 51 largest US Commercial Banks in terms of revenues. Use the information in this file to complete the following:

a. Compute the mean, median and standard deviation for the three variables: revenues, profits and number of employees.

b. Convert the data for each variable to z value. Consider Mellon Bank Corporation headquarters in Pittsburgh. How does it compare to the average bank in the study on the three variables? Discuss.

c. As you can see by examining the data and by looking at statistics computed in part (a), not all banks had the same revenue, same profit or the same number of employees. Which variable had the greatest relative variation among the banks in the study?

d. Calculate a new variable: profits per employee. Develop a frequency distribution and histogram for this new variable. Also compute the mean, median and standard deviation for the new variable. Write a short report that describes the profits per employee for the banks.

e. Referring to part (d), how many banks had a profit-per-employee ratio that exceeded 2 standard deviations from the mean?

Name	Revenues	Profits	Employees
CITICORP	34697	3591	93700
CHASE MANHATTAN CORP.	30381	3708	69033
BANKAMERICA CORP.	23585	3210	77000
NATIONSBANK CORP.	21734	3077	80360
J.P.MORGAN & CO.	17701	1465	16943
FIRST UNION CORP.	14329	1896	43933
BANC ONE CORP.	13219	1306	56600
BANKERS TRUST N.Y. CORP.	12176	866	18286
FIRST CHICAGO NBD CORP.	10098	1525	33962
NORWEST CORP.	9660	1351	55729
WELLS FARGO & CO.	9608	1155	33100
FLEET FINANCIAL GROUP	8095	1303	32317
U.S. BANCORP	6909	839	25858
PNC BANK	6859	1052	24814
BANKBOSTON CORP.	6727	879	21500
KEYCORP	6568	919	24595
BANK OF NEW YORK CO.	5697	1104	16494
WACHOVIA CORP.	5270	593	21652
NATIONAL CITY CORP.	5152	807	29841
MELLON BANK CORP.	5134	771	27500
SUNTRUST BANKS	4585	667	21227
MBNA	4524	623	17398
CORESTATES FINAN. CORP.	4379	813	18847
BARNETT BANKS	4102	255	21487
REPUBLIC NEW YORK CORP.	3738	449	5900
STATE ST. CORP.	3428	380	14199
COMERICA	3175	530	11000
BB&T CORP.	2598	360	9803
SOUTHTRUST CORP.	2503	307	10311
SUMMIT BANCORP	2367	371	8566
HUNTINGTON BANCSHARES	2324	293	9485
NORTHERN TRUST CORP.	2267	309	7553
MERCANTILE BANCORP.	2257	205	9510
FIRST OF AMER. BANK CORP.	2078	315	10622
CRESTAR FINANCIAL CORP.	1997	310	8215
FIFTH THIRD BANCORP	1924	401	6787
REGIONS FINANCIAL	1912	300	9227
FIRSTAR CORP.	1893	295	7755
UNION PLANTERS CORP.	1778	209	7711
MARSHALL & ILSLEY CORP.	1743	245	10227
POPULAR	1739	210	8854
AMSOUTH BANCORP.	1644	226	6400
FIRST TENN. NATL. CORP.	1609	197	8207
FIRST SECURITY CORP.	1503	206	7673
OLD KENT FINANCIAL CORP.	1306	180	6328
FIRST EMPIRE STATE CORP.	1258	176	4781
PACIFIC CENTURY FINANCIAL	1250	139	5114
PROVIDIAN FINANCIAL	1217	191	3884
SYNOVUS FINANCIAL CORP.	1215	165	7496
COMPASS BANCSHARES	1131	156	5060
FIRST NATL. OF NEBRASKA	1047	75	5200

Answer 1

ans::

as for given data

A) We will use excel to solve the data with all formulas provided.

sum all the value of revenue and divide 51 to find mean of revenue. similarly do for Profit and Employees.

	Revenues	Profits	Employees
Mean	6355	803	21530

For Median make revenue in ascending order and take the 26th value (51/2 = 25.5=26 which is the middle value). Similarlly proceed for profit and employee.

	Revenues	Profits	Employees
Median	3428	401	11000

for Standard deviation use the following formula

	Revenues	Profits	Employees
Std	7458	882	21269

B)

We take the population mean as

	Revenues	Profits	Employees
MELLON BANK CORP.	5134	771	27500

	Revenues	Profits	Employees
Stdev	7458	882	21269
n	51	51	51
Square root(n)	7.14	7.14	7.14
Stderr	1044.28	123.48	2978.31

	Revenues	Profits	Employees
Mean(Xbar)	6355	803	21530

	Revenues	Profits	Employees
MELLON BANK CORP.(mu)	5134	771	27500

	Revenues	Profits	Employees
Zvalue	1.17	0.26	-2.00

I have compared the average of all banks revenue, profit and employees with that of melon bank and got the zvalue using z test. There was no level of significance so based on the the level of sig we can compare. if I take .05 level of sig we get zcritical value as +or-1.96 for 2 tail. hence we can say that comparing the zvalue and zcritical we say there is a difference between employee of melon and the average of rest since -2<-1.96.

C)

CHASE MANHATTAN CORP. had the highest revenue and profit among the othe companies in the given data.

The difference between the revenue and average revenues of the data set is 26953.

The highest number of employee was found in NATIONSBANK CORP..

D)

Range		Frequency	Cumulative Freq
0	0.01	0	0
0.01	0.02	2	2
0.02	0.03	17	19
0.03	0.04	15	34
0.04	0.05	12	46
0.05	0.06	2	48
0.06	0.07	1	49
0.07	0.08	1	50
0.08	0.09	1	51

Mean	Median	Stdev
0.04	0.04	0.01

E)

Mean+2*stdev

0.037+2*0.014 = 0.064

Values with P/E ratio above 0.064

Name	Revenues	Profits	Employees	P/E	>2stdev
J.P.MORGAN & CO.	17701	1465	16943	0.086466	Yes
BANK OF NEW YORK CO.	5697	1104	16494	0.066933	Yes
REPUBLIC NEW YORK CORP.	3738	449	5900	0.076102	Yes

note:: part in b: " How does it compare to the average bank in the study on the three variables? Discuss", as I don't know how to compare it.

sol:  I have compared the average of all banks revenue, profit and employees with that of melon bank and get the zvalue using z test. Based on the the level of sig we can compare. if I take .05 level of sig we get zcritical value as +or-1.96 for 2 tail. hence we can say that comparing the zvalue and zcritical we say there is a difference between employee of melon and the average of rest since -2