SPC tools and techniques– part 2 & Fundamentals of Statistics—Part 1

  

1. In the article “The tools of Quality Part IV: Histograms” (Quality Progress, September 1990, Vol. XXIII, No.9, pp.75-78) data are presented on the gain of 120 amplifiers. These data are reproduced below. 

a) Construct a stem-and-leaf display step by step. Category Interval=1 (7,8,9,10,11 as stems, and decimal number as leaf) (3pts). 

b) Comment on the shape of the display in a. Can you make an assumption that the data follows normal distribution? Why? (2pt)

c) Construct a stem-and-leaf display step by step. Category Interval=0.5 (7.0≤X<7.5, 7.5≤X<8, 8.0≤X<8.5, ….) (1pts). 

  

8.1

10.4

8.8

9.7

7.8

9.9

11.7

8.0

9.3

9.0

 

8.2

8.9

10.1

9.4

9.2

7.9

9.5

10.9

7.8

8.3

 

9.1

8.4

9.6

11.1

7.9

8.5

8.7

7.8

10.5

8.5

 

11.5

8.0

7.9

8.3

8.7

10.0

9.4

9.0

9.2

10.7

 

9.3

9.7

8.7

8.2

8.9

8.6

9.5

9.4

8.8

8.3

 

8.4

9.1

10.1

7.8

8.1

8.8

8.0

9.2

8.4

7.8

 

7.9

8.5

9.2

8.7

10.2

7.9

9.8

8.3

9.0

9.6

 

9.9

10.6

8.6

9.4

8.8

8.2

10.5

9.7

9.1

8.0

 

8.7

9.8

8.5

8.9

9.1

8.4

8.1

9.5

8.7

9.3

 

8.1

10.1

9.6

8.3

8.0

9.8

9.0

8.9

8.1

9.7

 

8.5

8.2

9.0

10.2

9.5

8.3

8.9

9.1

10.3

8.4

 

8.6

9.2

8.5

9.6

9.0

10.7

8.6

10.0

8.8

8.6

Please be noted: you are not expected to use Excel Histogram function in this problem. In the next assignment, this function must be used. 

2. An experiment in chemistry looked at the effect of temperature on the solubility of salt in water. Below are data on the solubility of Potassium Chloride (KCL). Construct a scatter plot of the data and comment on the relationship between temperature and solubility using Microsoft Excel. (3pts)

  

Temp. °C

0

10

20

30

40

50

60

70

80

90

100

 

Solubility

29.6

28.0

33.6

38.1

34.2

42.6

44.8

48.1

56.5

55.4

62.9