Exercise1 - Business Statistics

8/20/2019 Exercise1 - Business Statistics

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Flavor FrequencyPineapple 50

Grapes 27

Orange 70

Mango 40

Strawberry 13

1. In a taste test conducted at S and M Grocery Mart, 200 people were asked tflavors of new tetra pack juice drinks and to report which one they preferred.!elow"

a. #raw a !ar chart.

Pineapple Grapes Orange

010

20

30

40

50

60

70

80

S and M Grocery Mart aste est $

%lavors

%re&uency of juice drinkers

!. #raw a pie chart.

25%

14%

20%

7%%re&uency of 'uice #rinkers on S and M Grocery Mart ast

Pine

Grap

Oran

Mang

Stra


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35%


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c. (hat flavor is preferred !y )ost drinkers*

d. (hat flavor is ne+t preferred !y juice drinkers*

e. (hat do the chart tell you a!out the sa)ple of juice drinkers*

f. If you were the owner of the rocery )art, what would !e the sinificance of thetaste test results*

The flaor preferre! by "ost !rin#ers is orane$

The flaor net preferre! by &'i(e !rin#ers is pineapple$

The (hart tells 's that "ost &'i(e !rin#ers preferre! the orange flaor a"ong others$ )owthe sa"ple of &'i(e !rin#ers$

The res'lts in!i(ate the !e"an!s of the (ons'"er oer (ertain flaors whi(h wo'l! helsatisfy s'(h !e"an!s$ +or ea"ple* the !e"an! for Orange,flaore! &'i(e !rin#s is hi


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o taste 5 differenthe rsult are listed

Mango Strawberry

sults

est $esults

pple

s

e

o

berry


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er* strawberry flaor is the least preferre! by

to i!entify the ol'"e of s'pply that willher than others$ Th's* s'pply for this flaor


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Job Category Frequency

Managerial -5

.leri(al /0

S#ille! wor#ers 45

ne"ploye! 15n!ere"ploye! 35

2. he uidance counselin office of a university conducted a five-year post radsurvey to deter)ine the types of jo!s their raduates were perfor)in. sa)pleraduates of the university was inteviewed. he responses were tallied and su)shown"

a. se an appropriate raphical techni&ue to su))ari/e and present the data.

!. pply the te+tual )ethod to )ake an interpratation a!out the perfor)ance of raudates.

Managerial .leri(al S#ille! wor#ers ne"ploye!

0

20

40

-0

0

100

Survey of the 'o! ateory Graduates erfor)in

'o! ateory

%re&uency of Graduates

n the fie,year post gra!'ation s'rey of the g'i!an(e (o'nseling offi(e* /0 o't of theirgra!'ates are perfor"ing (leri(al &obs$ l"ost half of the" fell either in "anagerial &obs or s#ill

wor#ers$ Generally* their gra!'ates are perfor"ing well sin(e -% only are 'ne"ploye! while 14'n!ere"ploye!$


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uationof 250ari/ed as

n!ere"ploye!

250!

are


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$atin %re&uency

(ellent 220

ery Satisfa(tory 175

Satisfa(tory 5

Poor 20

$atin %re&uency ercentae $ate

(ellent 220 44%

ery Satisfa(tory 175 35%

Satisfa(tory 5 17%

Poor 20 4%

3. he perfor)ance of all workers is !ein evaluated every end of 4 )onths !y thsuperiors in order to )onitor their efficiency and take necessary steps to i)prov&uality service is )aintained. he su))ary of perfor)ancce ratins of workers i

!elow"

a. se a pie chart to present the data iven. pply the necessary co)putations to )ake every saccurate. ou )ay use any colorin )aterials to enhance your presentation.

44%

35%

17%

4%

Summary of Performance Ratings of Worke

Excell

VerySatisf

Poor

!. Make a ta!ular presentation of the data with correspondin rate of percentae.


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eir. hus,listed

ctor

s

nt

atisfactoryctory


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ST6T 1 2 3 4 5 - 7 /

8G9: / 7- 72 -/ 75 -- /2 0

STTST.S - /5 75 70 71 7 71 75

6. In a university, le!ra is a prere&uisite for the Statistics su!ject. sa)ple of 15le!ra and Statistics of every student were recorded. he data were as follows"

a. #raw a scatter point diara) of the iven data.

0 1 2 3 4 5 - 7 / 10 11

50

55-0

-5

70

75

0

5

/0

/5

100

%inal Grades in le!ra and Statistics of 15

Students

%inal Grades

!. (hat relationship e+ists !etween the rades of students in le!ra and Statistics*

c. (hen a strudent ot the hihest score in le!ra, would you e+pect hi) to receive the hihest scor

;es$ The res'lts i"plie! by the graph tell 's that lgebra an! Statisti(s are asso(iate!$ St'!elgebra is "ore li#ely to re(eie the highest s(ore in Statisti(s$

positie (orrelation eists between the gra!es of st'!ents in lgebra an! Statisti(s$ i!e

the higher the st'!ent


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10 11 12 13 14 15

- 77 /0 77 2 70

/0 -/ 4 1 7 7/

tudents was drawn. he final rades in

12 13 14 15

students

8G9:

STTST.S

in Statistics*

ts who got the highest s(ore in

(e! by the graph whi(h shows that

e$


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G O+ P:SO 20 23 45 -0 47 3- 41 25

10 15 5 0 - 0 12M9: O+ )O:S SPT

T) T:T

5. he rowin internet users have forced different co)panies to sell their products onsituation, a statistician has u!dertaken a study to deter)ine how the ae of person is rhours of Internet use. rando) sa)ple of 15 persons was aked to ive their ae and tspend usin the Internet in a week. he aes of the respondents rane fro) 20 to 40 y

!elow"

a. 7)ploy the !est raph suita!le to the data.

!. Is there a linear relationship !etween two varia!les*

c. %ind the value of r.

d. What conclusion can be drawn about the relationshi ofthe two variables!

15 20 25 30 35 40 45 5

0

2

4

-

10

12

14

1-

8M97$ :% ;:$S S78 I8 ;7 I87$87 9

G7

8:. :% ;:$S S78

I8 ;7 I87$87

r "#$.%%&$%

;es$ egatie (orrelation eists between the two ariables$

The negatie (orrelation that eists between the two ariables signifies that as a person grewthe nternet !e(reases$


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3 43 20 22 30 5- 4

4 - 12 0 3 0

the (e!. #ue to thiselated to the nu)!er ofe nu)!er of hours theyars old. he data are listed

55 -0 -5

7# :8 ;7I$ G7

ol!er* the ti"e he or she spent in


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8o. of ;ousehold Me)!ers k(h

-

4

7

45

2

7

/

3

10

5

10

7

4. In an atte)pt to deter)ine the relationship !etween the nu)!er of )e)!ers in)onth of electricity, collect the data fro) 15 households !ased in your co))unit

a. $ecord the nu)!er of )e)!ers per household and the kilowatt use of electricity they had last )

!. #raw a raph of data.

1 2 3 4 5 - 7

0

50

100

150

200

250

300

350

400

450

$elationship 9etween k(h 1onsu)ption and the 8u)!

k(h 1onsu)ption


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c. (hat does the raph tell you a!out the relationship !etween the two varia!les*

d. (hat relationship e+ists !etween the two varia!les !ased on the co)puted value of r*

e. an you e+pect that the household with the least nu)!er of )e)!ers will have the least kilowahousehold with the !iest nu)!er of )e)!ers*

80M97$ :% ;:0S7;:=# M7M97

The graph in!i(ates that as the n'"ber of ho'sehol! "e"bers in(reases its #=h (ons'

r ? 0.@132121@501A@6Positie (orrelation eists between the two ariables$ n in(rease in the n'"ber of ho's#=h (ons'"ption$ lso* a !e(rease in the n'"ber of ho'sehol! "e"bers arises an !e(

;es$ ((or!ing to the graph aboe* the n'"ber of "e"bers hae an i"pa(t to the #=hleast n'"ber of "e"ber "ight (ons'"e the least #=h an! i(e ersa$


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nsu)ption

120

150

225

215

143145

/5

25-

2/5

122

345

2-

145

415

1/5

a fa)ily and the kilowatt used pery.

nth.

/ 10 11

r of ;ousehold Me)!ers


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t of electricity used* (hat a!out the

$S

"ption in(reases also or i(e ersa$

ehol! "e"bers arises an in(rease inrease in #=h (ons'"ption$

ons'"ption of a single ho'sehol!$ The


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'ear (umber of )ook

1//5 13*/2

1//- 14*25-

1//7 14*41

1// 14*7

1/// 14*443

2000 14*150

2001 13*//5

2002 13*-

2003 13*4//

2004 13*200

2005 12*41

200- 11*-3/

2007 11*-13

200 11*54

200/ 11*/01

A. he nu)!er of sold copies of the 9usiness Statistics !ook fro) 1@@5

latest edition> is listed in the ta!le !elow. se a line raph to present thinterpretation !ased on the iven record.

1//5 1//- 1//7 1// 1/// 2000 2001 200

10,000

10,500

11,000

11,500

12,000

12,500

13,000

13,500

14,000

14,500

15,000

15,500

(umber of Sold Coies of the )usines

(umber of )ooks Sold


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'ear

:!serva!ly, an increase in the sales of 9usiness Statistics !ook occurs fro) 1@@5 tpeak of the trend. ;owever, an alar)inly decrease occured fro) 1@@B to 200A whictrend. %ortunately, a su!tle increase fro) sales occured fro) 200A to 200@.


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s Sold

to 200@


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o 1@@B which is also the hihesth is also the lowest point of the


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Poulation

Singapore 4*5*-00

9ahrain 1*04-*14

So'th >orea 4/*044*7/0

etherlan!s 1-*423*431

Philippines 3*054*40

Swit?erlan! 7*252*331

>'wait 2*--*73

People


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!. (hat country has the reatest population* the least population*

c. (hich a)on the countries is considered the )ost crowded one* the least de

d. Make your interpretation !esed on the density of each country.

The (o'ntry whi(h has the greatest pop'lation is People


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+rea ,km-

707$1 -*4/

720 1*454

//*53 4/3

41*52 3/5

300*000 277

41*24 17-

17*1 151

/*5/-*/-1 13

/*-2/*0/1 31

103*000 3

/ensity ,Po.Per km-

unit volu)e. he ta!le !elow shows thein k)C>. 8otice that the density population

pe(ts :eport$

country. ut the applica!le leend.

of .hina (elan!

,

1*000

2*000

3*000

4*000

5*000

-*000

7*000ity

Pop'lation


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nse*

ensty op$ er "

hile (elan! has the least pop'lation$

least !ense$

sity relies not &'st in its pop'lation b't also to its


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hilippines pr-0B pr-0A

Total 15 years ol! an! oer Bin


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pr-0B pr-0A

"ploy"ent :ate B/2%D 53,084,000 52,236,586

ne"ploy"ent :ate B%D 4,616,000 4,174,414

pr-0B pr-0A

n!ere"ploy"ent :ate B%D 11,424,600 10,661,679

!. o)pare the fiures of pril 200A and pril 200B.

c. (hich year was considered !etter*

d. alculate how )any people were e)ployed and une)ployed.

e. ;ow )any people do you e+pect are workin not within their line of speciali/ation*

"ploy"ent rate on pril 2007 was higher by 0$-% than of pril 200$ )oweer* pril 2007


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B !y

D


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nt rate is

year$ f


31/34

ear Sinle

1/// -$-

2000 -/$2

2001 -/$4

2002 -/$7

2003 70$0

2004 -$7

2005 -$2

200- -$2

2007 -$2

200 -$7

10. he followin ta!le shows the list of the percentae of sinle and )arried wo)ehave jo!s outside their ho)es durin the period 1@@@-200B.

a. onstruct a line raph for sinle wo)en and another one for )arried wo)en.

1/// 2000 2001 2002 2003 2004 2005 200

-7

-7$5

-

-$5

-/

-/$5

70

70$5

ercentae of (orkin Sinle (o)en

ear

ercentae

5-

5

-0

-2

-4

ercentae of (orkin Married (o)en

ercentae


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!. naly/e the fiures for sinle and )arried wo)en with respect to the years.

c. (hat conclusion can !e drawn fro) workin sinle wo)en as you see the percentaes

d. #escri!e the percentae rates of the workin )arried wo)en.

1/// 2000 2001 2002 2003 2004 2005 200

52

4

ear

Obserably* the tren! of wor#ing single wo"en fla(t'ate oer the ten years ti"e while t(ontin'o'sly in(reases$ The highest per(entage of wor#ing single wo"en lies on the yefro" 2005,2007$ On the other han!* the highest per(entage of wor#ing "arrie! wo"en1///$

Single wo"en


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ro) 1@@@ to 200B*

- 2007 200

e tren! of wor#ing "arrie! wo"enar 2003$ ts lowest per(entage lieso(('re! in 200 while its lowest in

erio! of 2005 to 2007$ The

s as(en!$ Therefore* oer ti"e*

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Exercise1 - Business Statistics

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