Third, the researcher wishes to use numerical descriptive measures to summarise the data on each of the two variables: hours worked per week and yearly income. Hours per week Yearly Income ('000's) 18 43.8p 13 44.5 18 44.8 25.5 46.0 11.5 41.2 18 43.3 16 43.6 27 46.2 27.5 46.8 30.5 48.2 24.5 49.3 32.5 53.8 25 53.9 23.5 54.2 30.5 50.5 27.5 51.2 28 51.5 26 52.6 25.5 52.8 26.5 52.9 33 49.5 15 49.8 27.5 50.3 36 54.3 27 55.1 34.5 55.3 39 61.7 37 62.3 31.5 63.4 37 63.7 24.5 55.5 28 55.6 19 55.7 38.5 58.2 37.5 58.3 18.5 58.4 32 59.2 35 59.3 36 59.4 39 60.5 24.5 56.7 26 57.8 38 63.8 44.5 64.2 34.5 55.8 34.5 56.2 40 64.3 41.5 64.5 34.5 64.7 42.3 66.1 34.5 72.3 28 73.2 38 74.2 31.5 68.5 36 69.7 37.5 71.2 22 66.3 33.5 66.5 37 66.7 43.5 74.8 20 62.0 35 57.3 24 55.3 20 56.1 41 61.5 1. Prepare and display a numerical summary report for each of the two variables including summary measures such as mean, median, range, variance, standard deviation, smallest and largest values and the three quartiles. Notes: Use QUARTILE.EX command to generate the three quartiles. 2. Compute the correlation coefficient using the relevant Excel function to measure the direction and strength of the linear relationship between the two variables. Display and interpret the correlation value.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Third, the researcher wishes to use numerical descriptive measures to summarise the data on each of the two variables: hours worked per week and yearly income.
|
Hours per week
|
Yearly Income ('000's)
|
|
18 |
43.8p |
|
13 |
44.5 |
|
18 |
44.8 |
|
25.5 |
46.0 |
|
11.5 |
41.2 |
|
18 |
43.3 |
|
16 |
43.6 |
|
27 |
46.2 |
|
27.5 |
46.8 |
|
30.5 |
48.2 |
|
24.5 |
49.3 |
|
32.5 |
53.8 |
|
25 |
53.9 |
|
23.5 |
54.2 |
|
30.5 |
50.5 |
|
27.5 |
51.2 |
|
28 |
51.5 |
|
26 |
52.6 |
|
25.5 |
52.8 |
|
26.5 |
52.9 |
|
33 |
49.5 |
|
15 |
49.8 |
|
27.5 |
50.3 |
|
36 |
54.3 |
|
27 |
55.1 |
|
34.5 |
55.3 |
|
39 |
61.7 |
|
37 |
62.3 |
|
31.5 |
63.4 |
|
37 |
63.7 |
|
24.5 |
55.5 |
|
28 |
55.6 |
|
19 |
55.7 |
|
38.5 |
58.2 |
|
37.5 |
58.3 |
|
18.5 |
58.4 |
|
32 |
59.2 |
|
35 |
59.3 |
|
36 |
59.4 |
|
39 |
60.5 |
|
24.5 |
56.7 |
|
26 |
57.8 |
|
38 |
63.8 |
|
44.5 |
64.2 |
|
34.5 |
55.8 |
|
34.5 |
56.2 |
|
40 |
64.3 |
|
41.5 |
64.5 |
|
34.5 |
64.7 |
|
42.3 |
66.1 |
|
34.5 |
72.3 |
|
28 |
73.2 |
|
38 |
74.2 |
|
31.5 |
68.5 |
|
36 |
69.7 |
|
37.5 |
71.2 |
|
22 |
66.3 |
|
33.5 |
66.5 |
|
37 |
66.7 |
|
43.5 |
74.8 |
|
20 |
62.0 |
|
35 |
57.3 |
|
24 |
55.3 |
|
20 |
56.1 |
|
41 |
61.5 |
1. Prepare and display a numerical summary report for each of the two variables including summary measures such as mean,
Notes: Use QUARTILE.EX command to generate the three quartiles.
2. Compute the
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