QC Tools By Mahima Prasad
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Transcript of QC Tools By Mahima Prasad
Kaizen is a system in which every employee is encouraged to come up with small improvement suggestions in their area of work on a regular basis
This is a continuous exercise
INTRODUCTION:
“LEAN GURU” AND THE FATHER OF CONTINUOUS IMPROVEMENT (CI)
Masaaki Imai is known as the developer of Kaizen
KAI means 'change' or 'the action to correct'.
ZEN means 'good'
1. Quality
2. Effort
3. Involvement of all employees
4. Willingness to change
5. Communication
1. Seiko- Tidiness/Proper arrangement
2. Seiton- Orderliness
3. Seiso- Cleanliness
4. Seiketsu- Personal cleanliness
5. Shitsuke- Discipline
Identification of materials, equipment and tools, data and information which are necessary or not necessary
Discarding or giving another destination to unnecessary items and providing the necessary space for the necessary items which you require to perform the necessary task
It is not only essential to tidy the place but also arrange them in the orderly fashion.
Every equipment or data or anything should be placed in its appropriate and unique place.
It reduces confusion and avoids wastage of time.
Apart from a place being tidy and orderly it should be clean.
The shop floor should be free of wastage , oil spills, cotton wastes, etc.
The tools , machines and the entire organization should be free from dirt.
Organization should also identify and eliminate any source of dirt, dust or trash.
Maintaining good sanitary conditions and maintaining good personal hygiene.
A person should be clean and his cloths should be clean.
Seiketsu also talks about keeping good sanitary conditions in common places in an organization such as bathrooms, toilets, kitchen, etc.
Self discipline is the best disciplining strategy were one doesn’t need an external authority to discipline oneself.
Job discipline is the habit and skill development to perform the job according to standards, to observe company rules and policies at all times, fulfill required, written and other informal specification and requirement in the organization.
This habit of discipline is developed as a result of excursing mental, moral and physical strength.
Acceptance quality level is an inspection standard describing the maximum number of defects that could be considered acceptable during the random sampling of an inspection.
The defects found during inspection are sometimes classified into three levels: critical, major and minor.
Critical defects are those that render the product unsafe or hazardous for the end user.
Major defects can result in the product's failure, reducing its marketability, usability or saleability.
Minor defects do not affect the product's marketability or usability, but represent workmanship defects that make the product fall short of defined quality standards.
This is a method of cost reduction and productivity improvement.
The employees are working in the organization at different levels.
While on the job they get number of ideas in their mind to do some improvements.
Every improvement yields some gains To garner these gains suggestion scheme is
implemented.
1. Scheme Coordinator
2. Suggestion Scheme Committee
3. The Suggestion Evaluator
4. The Suggestor
1. Appoint suggestion committee and suggestion coordinator .
2. The suggestion committee should create suitable rulesto suit the company culture. These rules can be later amended.
3. The form is prepared and got printed4. Total sincerity and transparency should be displayed5. Take the membership of
(INSSAN INDIAN NATIONAL SUGGESTION SCHEMES ASSOCIATION)
Give a subject for each month Motivate employees to think about that subject.
Provide basic data for utilities that company is using.
Give token gift for each given suggestion.
Annual awards for different purposes can be announced
Respond to all written suggestions immediately in writing.
High light the suggestions publicly.
Award to be given immediately for best suggestions.
Establish categories for regular awards.
Awarding presentation should be big function.
Kaizen are generally a group activity
Suggestion Scheme is an individual activity
Kaizen focuses on pain areas
Suggestion scheme aims at cost reduction
Kaizen is small continuous improvement
Suggestion Scheme can give big benefits
Kaizen motivates employees and suggestion scheme focuses on award for cost reduction
A stem and leaf diagram provides a visual summary of your data.
This diagram provides a partial sorting of the data and allows you to detect the distributional pattern of the data.
Split the data into two pieces, stem and leaf.
Arrange the stems from low to high.
Attach each leaf to the appropriate stem.
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median time taken
stemleaf
3
4
5
6
7
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7
1
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7
3
1
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3
3
1
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6
3
1
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6
3
1
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6
3
1 8
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8
3
1 8
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8
3
1 8
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8
3 7
1 8
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8 8 1 9
3 7 4
1 8 3
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8 8 1 9 2
3 7 4
1 8 3
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8 8 1 9 2
3 7 4 8
1 8 3
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8 8 1 9 2
3 7 4 8
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8 8 1 9 2 5
3 7 4 8
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8 8 1 9 2 5 4
3 7 4 8
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median, quartiles and inter-quartile range
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8 8 1 9 2 5 4 3
3 7 4 8
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8 8 1 9 2 5 4 3
3 7 4 8 1
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
7 3 6 6 8 8 1 9 2 5 4 3 5
3 7 4 8 1
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5
3 7 4 8 1
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6
3 7 4 8 1
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4
3 7 4 8 1
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4
3 7 4 8 1 2
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3
3 7 4 8 1 2
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
Completion times
Answer (a):- (1) key: 4|7 means 47
(2) put values into preliminary diagram:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
Question:- 29 students were set a simple task. Their completion times to the nearest second were:
47 61 53 43 46 46 68 48 72 57 48 54 41 63 49
42 58 65 45 44 43 51 45 38 46 44 52 43 47
(a) set these data into a stem and leaf diagram
(b) find the median
(3) re draw diagram with leafs in numerical order:
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7 8
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7 8
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7 8
1
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7 8
1 3
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7 8
1 3 5
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7 8
1 3 5 8
Completion times
Completion times
Answer (a):- (3) re draw diagram with leafs in numerical order:
3
4
5
6
7
8
7 3 6 6 8 8 1 9 2 5 4 3 5 6 4 3 7
3 7 4 8 1 2
1 8 3 5
2
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7 8
1 3 5 8
2
4|7 means 47
Completion times
Completion times
2
129
Answer (b):-
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7 8
1 3 5 8
2
Completion times
The median is the middle value:
15th
Median = 47
4|7 means 47
i.e. 15th value
There are 29 values
Answer (b):-
3
4
5
6
7
8
1 2 3 3 3 4 4 5 5 6 6 6 7 7 8 8 9
1 2 3 4 7 8
1 3 5 8
2
Completion times
Lowest
Range = Highest - Lowest
4|7 means 47
Highest
Range = 72 – 38 = 34
Thank you
