Statistics

Statistics

Exercise week 4

A manufacturing company produces u shape brackets for rain-water downpipes for a major plumbing supplier. The customer specifies they want the bracket to be between 21.10 cm and 21.90cm. A recent sample of 50 items from the production line yielded the results in the sample data given below.

S.no

length in cm

1

21.11

2

21.13

3

21.14

4

21.19

5

21.2

6

21.21

7

21.27

8

21.29

9

21.29

10

21.3

11

21.33

12

21.34

13

21.35

14

21.35

15

21.36

16

21.36

17

21.36

18

21.36

19

21.37

20

21.37

21

21.37

22

21.37

23

21.37

24

21.38

25

21.39

26

21.39

27

21.39

28

21.39

29

21.39

30

21.4

31

21.41

32

21.41

33

21.43

34

21.44

35

21.45

36

21.46

37

21.46

38

21.48

39

21.49

40

21.49

41

21.49

42

21.5

43

21.53

44

21.54

45

21.54

46

21.54

47

21.55

48

21.56

49

21.58

50

21.58

a. Calculate a five figure summary of the data (minimum, first quartile, median, third quartile, maximum).

Lower Quartile

21.35 cm

Upper Quartile

21.48 cm

Median

21.39 cm

Min

21.11 cm

Max

21.58 cm

b. Construct a box plot.

c. Calculate the mean

The of the given data is 21.389cm

d. How would you describe the symmetry or skewness of the sample distribution?

The data sample given is left skewed and it shows that the data is inclined towards the lower side of the sample; which is the lower quartile. It can be observed from the box and whisker diagram presented above that the median of the data is 21.39cm and the lower quartile of the data is 21.35, which shows the difference of 0.04. However on the other hand if we look at the upper quartile, the figure for it is 21.48, where as the median is 21.39. This shows that the difference between the upper quartile and the median is 0.09. This further leads us to the conclusion that the difference of skewness is 0.05 among the two differences.

e. Calculate the variance and standard deviation of sample.

Mean

21.389

Variance

0.013

Standard Deviation

0.116

f. Calculate the z scores for the minimum specification (21.10cm) and the maximum specification (21.90cm)

Values

z score

21.1

-2.4961

21.9

4.4135

g. Using Chebychev's rule below what can you conclude from the sample about the manufacturer's ability to meet the specification?

Chebychev's rule

25.40%

Exercise week 6

Question 1

An experiment consists of throwing two coins simultaneously. The event of interest

(considered a success) consists of throwing two heads. List the possible outcomes (The set of possible outcomes is often referred to ...