statistics 1

Case 1

' ; CAS ES . . , , ~ ii / Kt~ Century National Bank •.

"; The following · case wlll appear In' subsecJuent review sec- ~tlons. Assume -that you work In the Planning Department of .;_the.Century National Bonk and report to Ms. Lamberg. You -Wlll'need.to do soine data analysis and prepare a short writ- , _en··report-Reniember, .fv1r. Se/lg IS'th~ president of the bank,

~ r$O you will want to ensure that -your report Is complete and· :.,,.. accurate.•A c;opybf.the data appears 'fn•Appendlx A:6. ·

'.~: Cent ury National Bank -has.offices· In several cities in ·:. : the • Mldwest-: and ·the ,southeastern µart of the United :. States. Mr,· Dan· Sellg ,....-presldent and ·CEO,' would like to ; ~ know the• characteristics· of his checking account ·custom- · .. , - ers .- What-1s the balance:·•of:a'typlcal customer? ·

1 ·\· · ' How many other ,ba.nkr -.ser;vlces 1 do the-checking ac- ~-!-count customers use?: Do the,customers :use.the-ATM ser- · · t f:vice and, :lf 50·, how often? What.'about.debit.·cards? Who · ' · uses t hem~ ··and ho'.v•.often -are·•they. used?. _ . . :_; _ .. To ·.better understand the .austomers;·. Mr. Selig asked · )rMs.:_Wendy Lambergr dlrector of pl~nnlng, to sele~ a sam~ · ple•pf ,t:ustomers .and._pr.epare a. report. _To begin, she. has

·~ppolnted a team-from her:staff,::You, are .the .head of the:; team and responsible for·preparlng the report.· You -select a· ,.':'~ndornsample,of 60 customers:· lri.additlon.to the balance '. } f:r ·each'~account-at the end of.- last month; you· determine ·

C1)< the·number of ATM .(automatic teller -machine). transac, ~pii,s In t he last montti; .'(2) -the.number-.of other, bank.ser> _ Ices· (a .savlngs·· account; a· certificate ·of :deposit;-etc:). the ,

'~Ustomer uses; (3) whether:.the·: customer has.a· debit ·card ' . Jthi~ ls .. a ban ~ service In. which charges are made·directly,to '. ·. ~e··customer.'s account); and (4) Whether or not·lnterest Is ~aid · on the checking ·accounL The• sample ,includes cus~ .tmet~ .. _from_, t~e bra ~ches· lri : Cincinnati, 1 Ohlo;,:Atlanta ;

· t;:7~rg1a, .Lou1sv1lle;, Kentuckyj,.and· Erle, Pennsylvania:·.

j l•. ·Develop a ·graph or table that portrays the checking ~r: balances.· What Is the. balance· of a typical customer?

~- Do many customers- have: more than $2,000iin their ,.< .- _ a_ccounts? Does .it appear that there is ·a·difference In . · the distribution of the accounts among the four : . , · -branches? Around what- value do the account ba l- _ .. -· · ances tend. to ·cluster? ·

)./ i!it,;,-.

2: ~Determine ·the :mean. and median of the checking ac- count ·balances .. Compare the mean and the median ba/ances ·Jor the four branches. Is there a difference among the•branches? Be sure to explain the difference between the mean and the median in your report / :

3. ~Determine.Jhe range an d. the:tstandard.devta tfon of the check/ ng:account balances: What do th e, first an d thlrd,: quartiles: show.? Determine the· coefflcle nt .of skewness -·and . Indicate , what It shows. ·- Because Mr . .Selig ·does;•not:deal with statistics dally, include a 1 brief descriptlon •and interpretation of the, standa rd I deviation and .other measures. •:

Case 2

CASES . . -:--t- ~ ... -.. ~ :. .... : . '·· ·, .": .-..

"( A. Century. National .Bank·~ Refer · to:•the·,Gentory·-Natlona l: B'ank data .> ,1s· ·it' reasonable thatthe distributloni of checking·account balances' approx- lmatesr-a· normal :-pr.obabi lity,,distributlon?.·Determlne t he . mean -and the:,standard: deviation· .for the ,sample •of 60 customers .. Compare the' actuahdistribution-wlth the· th eo- retical . distribution~ Cite sornt!speciflc examples and com- ment ·on,your, findings ;,- . .

Divide .the .account balances·-irito three· g roups, of about.20 each ,:-with the smallestthlrd of the . balances in the first group; the1:mtddle·third In t9,e· second group, and those with ·the -largest balan ces in tfie third group. Next, . develop a table that-shows. the: number In each of the e;at-.

egories of the' account~balances by bran ch~ Does· it ap- pear that accounfb_alances are·re\ated t o the branc h? Cite some e~ampl~s·:~n~~~o~men~ on ,your,fin d lngs.