Week 2 - Portion Covered.(Refer TEXT BOOK)

Assignment details Quick Access to detailed Solutions

Page 17: 2-1, 2-2.

Page 24 : 2-12

Page 35: 2-22

Page 35: 2-23Page 53: 2-34Page 53: 2-35

Page 60: 2-44

Page 17 Table 2-1 & 2-2

Page 24 2-12

Page 35 2-22page 35 2-23Page 53 Q 2-34Page 53 Q 2-35

Page 60 Q2-44

page 17

Table 2-1

High school and college grade point average of 20 Collge seniors

H.S. College Average(Mean)3.6 2.5 College 3.190.6 2.7 H.S. 3.072.7 2.23.7 3.2

4 3.83.5 3.63.5 3.82.2 3.53.9 3.7

4 3.93.4 3.62.9 33.9 43.2 3.52.1 2.52.2 2.83.4 3.43.6 32.6 1.92.4 3.2

Table 2-1

Pounds of pressure per square inch that concrete can withstand

Pressure per square inch(in Pounds)2500.22500.82490.52499.22506.42497.82502.52504.12498.32499.92496.92503.22508.22496.72508.42500.82496.92500.82490.42502.32491.62495.32502.22493.42491.32503.72497.12508.12500.72509.52501.32499.72493.8

25022498.4

25002505

2497.82502.52498.1

Average(Mean)2499.895

Page 24

Q 2-12

Speeds of 45 motorists(Raw data)

Speeds

1532

45464239

684718

314849565239486961444238

525558625848565848475237642955

15-25 26-36 37-47 48-58 59-69

34

12

18

8

Histogram for Table 1

Class interval

Freq

uenc

y

382962496918615549

15-25 26-36 37-47 48-58 59-69

34

12

18

8

Histogram for Table 1

Class interval

Freq

uenc

y

Speeds of 45 motorists(Raw data)

Modus Operandi

1. find max and min values from raw data, choose a start value.2. determine range of each class interval, for given number of intervals

3. group data pertaining to each class interval4. determine frequency for each class interval5. determine relative frequency6. determine percentage frequency

7. plot histogram8. perform analysis9. answer questions

Answers:a. Orange county motorists do not follow the US DOT reportsb. Table 2:- Relative percentage frequency distributionc. 66.67% of the motorists drive within the range of 36mph and 59 mph Table 1:- relative frequency distribution

15-25 26-36 37-47 48-58 59-69

34

12

18

8

Histogram for Table 1

Class interval

Freq

uenc

y

15-25 26-36 37-47 48-58 59-69

34

12

18

8

Histogram for Table 1

Class intervalFr

eque

ncy

Number of equal class intervals Table 1. (For 5 equal classes)

511 15-25

Min 15 26-36Max 69 37-47Start Value 15 48-58

11 59-69

5

Table 2. (For 11 equal classes)

15-1920-2425-2930-3435-39

Analysis 1 40-44Percentage of motorists who exceed 55mph 45-49

Table 2 35.56% 50-54Analysis 2 55-59

Percentage of motorists who drive within 36mph and 59mph 60-64Table 1 66.67% 65-69

Analysis 3Proportion of motorists who drive within 36mph and 59mph

Table 1 0.67

Category / Class

Incremet (Class Width) for 5 equal in tervals

Incremet (Class Width) for 11 equal in tervals

Category / Class

15-25 26-36 37-47 48-58 59-69

34

12

18

8

Histogram for Table 1

Class interval

Freq

uenc

y

15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69

3

0

2 2

53

11

3

8

53

Histogram for Table 2

class intervals

Freq

uenc

y

15-25 26-36 37-47 48-58 59-69

34

12

18

8

Histogram for Table 1

Class interval

Freq

uenc

y

Table 1. (For 5 equal classes)

Lower Upper Frequency Relative Frequency15 25 3 0.07

26 36 4 0.0937 47 12 0.2748 58 18 0.4059 69 8 0.18

Total 45 1

Table 2. (For 11 equal classes)

Lower Upper Frequency PercentFrequency15 19 3 0.0720 24 0 0.0025 29 2 0.0430 34 2 0.0435 39 5 0.1140 44 3 0.0745 49 11 0.2450 54 3 0.0755 59 8 0.1860 64 5 0.1165 69 3 0.07

Total 45 1.00

15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69

3

0

2 2

53

11

3

8

53

Histogram for Table 2

class intervals

Freq

uenc

y

Table 1. (For 5 equal classes)

6.67% 6.67%

8.89% 15.56%26.67% 42.22%40.00% 82.22%17.78% 100.00%

100.00%

Table 2. (For 11 equal classes)

6.67% 6.67%0.00% 6.67%4.44% 11.11%4.44% 15.56%

11.11% 26.67%6.67% 33.33%

24.44% 57.78%6.67% 64.44%

17.78% 82.22%11.11% 93.33%

6.67% 100.00%

100.00%

percentage relative frequency

Cumulative percentage frequency

percentage relative frequency

Cumulative percentage frequency

Page 35

Q2-22

2637

40181445326831372032

15

2746446258304222264441345550632922

Customer Age

Modus Operandi

1. find max and min values from raw data, choose a start value. 52. determine range of each class interval, for given number of interval

Min4. determine frequency for each class interval Max5. determine relative frequency Start Value6. determine percentage frequency Incremet (Class Width) for 5 e7. plot histogram8. perform analysis9. answer questions

Answers Analysis

middle aged customers:

old agedyoung

Number of open ended class intervals

3. group data pertaining to each class interval, form an open ended classification

a. it can be clearly seen from table 1 and its histogram that the majority of the customers fall in the age group 20 to 49 with ech group having 7 customers each(20-29, 30-39, 40-49)

it is evident that majority of Symphony's customers are middle aged, followed by older and the least market is in the young aged

TABLE 1(Frequency distribution for custumers in each age group)

Age Groups Lower Upper Frequency10-19 10 19 320-29 20 29 7

14 30-39 30 39 768 40-49 40 49 710 50-Older 50 Older 610 Total 30

70.00%

20.00%10.00%

10-19 20-29 30-39 40-49 50-Older

3

7 7 7

6

Histogram for table 1

Age Range

freq

uenc

y

TABLE 1(Frequency distribution for custumers in each age group)

Relative Frequenc0.10 10.00% 10.00%0.23 23.33% 33.33%

0.23 23.33% 56.67%0.23 23.33% 80.00%0.20 20.00% 100.00%

1 100.00%

Percentage relative frequency

Cumulative percentage frequency

10-19 20-29 30-39 40-49 50-Older

3

7 7 7

6

Histogram for table 1

Age Range

freq

uenc

y

page 35

Q 2-23

Customer Purchase amount grouping

upper limit lower limit $ Spent Frequency

0.00 0.99 0-0.99 50 501.00 3.999 1-3.999 240 290

4.00 6.999 4-6.999 300 5907.00 9.999 7-9.999 460 1050

10.00 12.999 10-12.999 900 195013.00 15.999 13-15.999 1050 300016.00 18.999 16-18.999 1150 415019.00 21.999 19-21.999 980 513022.00 24.999 22-24.999 830 596025.00 27.999 25-27.999 780 674028.00 30.999 28-30.999 760 750031.00 33.999 31-33.999 720 822034.00 36.999 34-36.999 610 883037.00 39.999 37-39.999 420 925040.00 42.999 40-42.999 280 953043.00 45.999 43-45.999 100 963046.00 48.999 46-48.999 90 9720

Cumulative frequency

Modus Operandi

Outliers3. group data pertaining to each class interval.

5. determine relative frequency6. determine percentage frequency7. plot histogram8. perform analysis outliers9. answer questions

new Incremet (Class Width) 9

1. reduce number of intervals and determine new range of each class interval

4. determine frequency for each class interval for both old and new grouping

New Simplified grouping

Lower Upper Frequency Relative Frequency

0-0.99 0.00 0.99 50 0.011-9.999 1.00 9.999 1000.00 0.12

10-18.999 10.00 18.999 3100.00 0.3619-27.999 19.00 27.999 2590.00 0.3028-36.999 28.00 36.999 2090.00 0.2437-45.999 37.00 45.999 800.00 0.0946-48.999 46.00 48.999 90 0.01

Total 8670 1

Spending groups

0-0.99 1-9.999 10-18.999 19-27.999 28-36.999 37-45.999 46-48.99950

1000.00

3100.00

2590.00

2090.00

800.00

90

histogram for table 1

spending groups

freq

uenc

y

0.58%0.12

0.360.300.240.09

1.04%100.00%

Percentage relative frequency

Page 53

Q 2-34

Given frequency distribution for length of phone calls made

upper limit lower limit1.00 7.00 1-7 458.00 14.00 8-14 32

15.00 21.00 15-21 3422.00 28.00 22-28 2229.00 35.00 29-35 1636.00 42.00 36-42 1243.00 49.00 43-49 950.00 56.00 50-56 5

Length in minutes

Frequency

Table 1

Modus Operandiupper limit

1. find max and min values from raw data, choose a start value. 12. determine range of each class interval, for given number of interval 8

154. determine frequency for each class interval 225. plot histogram 295. perform analysis 366. answer questions 43

50

Answers

c. As discussed above, the order will help in saving time.

3. group data pertaining to each class interval, form an open ended classification

a. The shape of the histogram is left skewed-the right tail of the distriburion is considerably longer than the left tail. There is a decrese in the frequency as the length of the calls increase with the exception of 15-21 min range.

b. Since the frequency with which the longest calls are made are low, they should be allowed to make calls first, followed by higher frequency callsers.

1-7 8-14 15-21 22-28 29-35 36-42 43-49 50-56

45

3234

22

16

129

5

Telephone calls made

length of calls in mins

freq

uenc

y

lower limit Frequency7 1-7 45

14 8-14 32

21 15-21 3428 22-28 2235 29-35 1642 36-42 1249 43-49 956 50-56 5

Length in minutes

1-7 8-14 15-21 22-28 29-35 36-42 43-49 50-56

45

3234

22

16

129

5

Telephone calls made

length of calls in mins

freq

uenc

y

page 53

Q 2-35

Raw Data of ages

Ages6665

96807193669675616961

51

845873778969925756557896

Modus Operandi

Min1. find max and min values from raw data, choose a start value. Max2. determine range of each class interval, for given number of intervals Start Value

3. group data pertaining to each class interval4. determine frequency for each class interval5. determine relative frequency6. determine percentage frequency7. plot histogram8. perform analysis9. answer questions

Answers Analysis

Dollars charged per person

total fee collectedPaid by remaining residents aft

Incremet (Class Width)

a. 80% of the residents would be eligible for no fee as can be seen from the ogive curve, the only demography lying in the non fee waivier is in the rage 50-59, wgich accounts for only 20 % of the residents

b.fee for 25 residents=$12. Total fee collected is $300. therefore the remaining residents would have to pay $60 to cover the same total cost

Table 1(Frequency distribution of age groups)

51 Lower Upper Frequency96 50-59 50 59 5 0.20 20.00%50 60-69 60 69 7 0.28 28.00%

10 70-79 70 79 5 0.20 20.00%80-89 80 89 3 0.12 12.00%90-99 90 99 5 0.20 20.00%

Total 25 1 100.00%

Dollars charged per person $12.00

total fee collected $300.00Paid by remaining residents aft $60.00

Age Category / Class

Relative Frequency

percentage relative frequency

50 60 70 80 90 100 110

20.00%

48.00%

68.00%

80.00%

100.00%

Cumulative percentage frequency(Ogive) for age

Age

Table 1(Frequency distribution of age groups)

20.00%48.00%

68.00%80.00%

100.00%

Cumulative percentage frequency

50 60 70 80 90 100 110

20.00%

48.00%

68.00%

80.00%

100.00%

Cumulative percentage frequency(Ogive) for age

Age

Page 60

Q 2-44

Raw Data Meaningful informationIncome Education Row Labels Min of Income Max of Income

17000 High School 1 year college 14400 2020020800 B.S. 10th grade 14400 1440027000 M.A. 11th grade 17600 1760070000 M.D. 2 years college 17200 2240029000 Ph.D. B.A. 19600 3440014400 10th grade B.S. 20800 3280019000 High School High School 17000 3040023200 M.A. Law Degree 52000 7600030400 High School M.A. 23200 2700025600 B.A. M.D. 70000 10000021200 B.S. M.S. 36200 3620028000 B.S. Ph.D. 29000 6400030200 High School Grand Total 14400 10000022400 2 years college

100000 M.D. Answer76000 Law Degree The grouping of data do provide a more meaningful information of the data and can be analysed for further inferences44000 Ph.D.17600 11th grade25800 High School20200 1 year college17200 2 years college19600 B.A.36200 M.S.18400 2 years college34400 B.A.26000 High School52000 Law Degree64000 Ph.D.32800 B.S.

Count of Income Income range2 14400-20200 Used pivot table1 14400-144001 17600-176003 17200-224003 19600-344004 20800-328006 17000-304002 52000-760002 23200-270002 70000-1000001 36200-362003 29000-64000

30

The grouping of data do provide a more meaningful information of the data and can be analysed for further inferences