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Use a scale that goes up to 130 km/h so that you can fit the second data set on it also.
On average Rockall experience higher wind speeds as compared to North…
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Wind speed data has been collected from two different weather stations over the of fifty days of stormy weather. panoramio.com Stormy Weather on the Baltic Sea
Rockall
Raw data is collected from Rockall- the wind speeds, measured in km/h on the fifty days in the study are recorded, in ascending order, in the table below:
23
24
26
29
30
30
34
35
38
39
42
46
47
48
49
49
50
51
51
53
53
55
56
58
59
61
62
64
65
68
68
68
69
70
73
74
74
75
77
81
81
82
85
86
89
90
90
91
94
95
 Find the mean, mode and median wind speeds, and comment on your findings.
Median = 60
Mode = 68
Mean = 60.14
The mean, mode, and median are all different and hence the data is concluded not to assume Gaussian distribution; rather, the data shows a slightly skewed distribution.
Use Excel to find the standard deviation of the wind speeds, and explain its relevance
Standard Deviation = 20.42009
Standard deviation shows how close data are to the average. In this case, the standard deviation is rather larger showing a sparsely distributed data.
Find the upper and lower quartiles of the data, and use them to draw a box and whisker diagram of the wind speeds. Use a scale that goes up to 130 km/h so that you can fit the second data set on it also.
Lower Quartile
47.25
Minimum
23
Median
60
Maximum
95
Upper Quartile
74.75
20 Marks
North Utsire
The wind speed data from North Utsire is given as grouped data:
Wind speed (w km/h)
Frequency
30 ≤ w < 40
15
40 ≤ w < 50
12
50 ≤ w < 60
8
60 ≤ w < 70
4
70 ≤ w < 80
2
80 ≤ w < 100
6
100 ≤ w < 130
3
Find the mean wind speed.
Wind speed (w km/h)
x
di
Frequency
fdi
30 ≤ w < 40
35
-30
15
-450
40 ≤ w < 50
45
-20
12
-240
50 ≤ w < 60
55
-10
8
-80
60 ≤ w < 70
65
0
4
0
70 ≤ w < 80
75
10
2
20
80 ≤ w < 100
90
25
6
150
100 ≤ w < 130
115
50
3
150
50
-450
Mean
56
Mode
37.83
Draw a histogram to represent the distribution of wind speeds.
Create a cumulative frequency table, and from it, draw a cumulative frequency curve. Use the curve to find the median and upper and lower quartiles.
Wind speed (w km/h)
Frequency
x
%
30 ≤ w < 40
15
15
30
40 ≤ w < 50
12
27
54
50 ≤ w < 60
8
35
70
60 ≤ w < 70
4
39
78
70 ≤ w < 80
2
41
82
80 ≤ w < 100
6
47
94
100 ≤ w < 130
3
50
100
What do the mean, median and quartiles tell you about the distribution of wind speeds in North Utsire?
Use the median and quartiles to draw a box and whisker diagram on the same scale as the one for Rockall.
Lower Quartile
33
Minimum
30
Median
44
Maximum
130
Upper Quartile
60
20 Marks
Analysis and Comparison
What conclusions can be drawn from the measures of central tendency for Rockall and North Utsire?
On average Rockall experience higher wind speeds as compared to North Utsire. However, looking at the modes, Rockall has a mode of 68 while North Utsire has a mode of 37.83.Going by the modes, it would be expected that higher wind speed is more common in Rockall as compared to North Utsire. Similarly, using the medians, Rockall has a median of 60 and hence higher wind speeds will be expected as compared as compared to North Utsire which has a median wind speed of 44. The maximum values however shown that while North Utsire does not high wind speeds most of the time, there are a few instances where it experiences the highest wind speeds.
What differences are there between the quartiles for Rockall and North Utsire? What can you conclude from these differences?
Like is the case with other measures, Rockall experiences a marginally higher lower quartile as compared to North Utsire showing reduced prevalence of low speed winds for Rockall. It further exhibits a higher upper quartile showing high prevalence of high speed winds.
How is this shown by the Box and Whisker Plots? What extra information do those graphs give you?
This finding is reflected in the box and whisker plot whereby for the case of Rockall, the whisker plot shows closeness of the highest value and the upper quartile. However, for North Utsire, the plot shows a big difference between the upper quartile and the maximum value. The graph further shows that wind speeds in North Utsire are mainly concentrated at the lower speeds with spontaneous occurrence of high speed winds.
What overall conclusions can be made about the weather conditions in Rockall and North Utsire?
Rockall weather station values individual wind measurements while North Utsire prefers estimated wind speeds falling within specific ranges.
Describe what else the various calculations and graphical representations have told you about the wind speeds in North Utsire and Rockall.
The calculations and graphical presentations reveal that measures of central tendency are not in themselves, sufficient enough to draw conclusions with reference to a particular weather condition. While the means of the two stations fall closely, it is evident that the areas exhibit marginally different weather conditions. In essence, it highlights the importance of looking at all the measures before drawing conclusion about the weather of a particular place.
Draw comparisons between the two weather stations.
In general, Rockwall weather station records more precise and raw data as compared to North Utsire and as such offer a more realistic representation of the weather of a place. Read More
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