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- 1. Data Presentation in a Bar Chart

Notes on the Sources of Data

The data above was collected by the Met Office, which is the National Weather Service for the United Kingdom. The organization has been engaged in weather forecasting and climate change for at least 20 years. The Met is significantly involved in public weather service through providing information and extreme weather warnings in order to help the UK residents to undertake informed decisions in such cases. The Met also collaborates with global organizations in offering vital services, ensuring that there is global understanding using research and being involved in collaborations. In addition, The Met offers objective and impartial data to the policy makers within the United Kingdom and European Union. This is arguably evident in the archives of their scientific publications, annual and scientific reports about weather. Since the data is from a reputable, it can be inferred that the data is reliable and can be used for analysis of the weather conditions within the United Kingdom.

The above bar chart shows a comparison of the mean temperatures for 1969 and 1996 for Northern Ireland. The data source indicates that allowances have been made the effects associated with topographical, coastal and urban effects, in cases whereby such relationships have been identified to exist. The seasons include winter, which spans from December to February; spring, which spans from March to May; summer, which spans from June to August; and autumn, which spans from September to November. The monthly values presented in the chart have been ranked to 1 decimal point and the seasonal values to 3 decimal points. The temperatures are displayed in Degrees Celsius. The following section conducts an analysis on the data sets presented on the chart with the main objective of determining which of the years was hottest.

- 2. Data Analysis on the Data Sets to Assess which of the Two Years was the Hottest

Assessment of the statistical data for the two years requires the use of a number of statistical calculations to determine the degrees of hotness for Northern Ireland during the two selected years. A fundamental approach that can be used to assess measure of hotness of the two years to determine the frequency of higher average monthly temperatures for the two years under study. From the chart, it can be observed that during January, February, March, April, September, November of 1996 were relatively hotter compared to the same months of 1969. The rest of the months were relatively hotter during 1969 than 1996. Such an approach does not provide adequate evidence to infer which of the two years was the hottest.

In terms of the average seasonal temperatures, winter, spring and autumn of 1996 were relatively hotter compared to 1969, with only the summer of 1969 being hotter compared to 1996. On seasonal averages, it can be inferred that 1996 was the hottest when compared with 1969. In addition, the annual average temperature for 1996 was relatively higher compared to the 1969 annual average temperature. The inference from the two analyses basing on the seasonal and annual average temperatures is that 1996 was relatively hotter when compared to 1969.

The hottest month in 1969 was July, with a mean temperature of 18.6. The coolest month during 1969 was February, with a mean temperature of 3.7. This implies that the temperature range for 1969 was 14.9. For the case of 1996, the hottest month was July, with a mean temperature of 18. The coolest month was December, with an average temperature of 6, implying that the temperature range for 1996 was 12. Basing on the temperature variations in terms of range, it can be inferred that 1996 was relatively hotter compared to 1969 because its temperature range is lower compared to the 1969 temperature range. This implies that the distribution of the monthly temperatures is equally spread throughout the year, making it the hottest of the two years. Range is used in this analysis because it indicates the scope of distribution of the average monthly temperatures. The analysis using the range of the monthly average temperatures serves to indicate that 1996 was the hottest of the two years.

With regard to the average seasonal temperatures, 1996 had the hottest winter, summer, autumn and spring than 1969. This observation clearly indicates that 1996 was relatively hotter than 1969. The range of the average seasonal temperatures during 1996 was 6.45 while the average seasonal temperature for 1969 was 12.24. This is a further indication that 1996 was hotter than 1969.

Statistical variance can also be used to assess the level of hotness in Northern Ireland during the selected years (Brase 2011). Variance is used for determining how far the data sets are spread out about the average. With regard to the definition of variance, a small variability implies more stable temperatures, which implies that a year having small variance is hotter compared with the year that has less variance. The following table shows the computations for variability of the average monthly temperatures for 1969 and 1996.

The annual average monthly temperature for 1969 is given by the following:

[6.8 + 3.7 + 11.1 + 13.5 + 17.2 + 18.6 + 17.9 + 15.9 +15.1 +7.1+ 6.7] /12 months = 11.72

The annual average monthly temperature for 1996 is given by the following expression:

[7.2+6.5+7.2+11.6+12.4+16.9+18+17.6+16.9+13.3+8.2+6] /12 months= 11.83

Table 1: Temperature Variability during 1969

Sum of the square of the deviation from the mean = 313.3885

Variability of the average monthly temperatures for 1969 is given by 313.3884/12 = 26.1157

Table 2: Temperature Variability for the Year 1996

Sum of the square of the deviation from the mean = 253.286

Variability of the average monthly temperatures for 1969 is given by 253.286/ 12= 21.1071

From the variability analysis of the average monthly temperature, it is arguably evident that 1996 has lower variability when compared to 1969. This implies that 1969 had more stable temperatures, and therefore 1996 was hotter than 1969.

- Limitations of the Data Collected as a Measure of Hotness

The first significant limitation associated with the collected data as a measure of hotness is mainly due to the limitations imposed by the use of mean value in analysis. The most significant stipulation when using the average values is that there is the likelihood that they can be skewed by the presence of absence of a single observation if it is widely distributed from the mean value. In the light of this view, the average monthly temperatures do not take into consideration the temperature variability within the months (Johnson & Gouri 2009). For instance, there is a possibility that the highest daily temperature was above the average monthly temperature and the lowest daily temperatures were considerably below the lowest average monthly temperature recorded. This implies that temperature variability computed using monthly averages do not accurately reflect the actual statistics observed. It is a fact that daily temperature observations cannot be normal in the sense that the mean, median and mode all have the same value. Temperature observations are characterized by extreme scores that are likely to distort the mean value of the monthly temperatures. Therefore, a high number of outliers in daily temperatures used in computing the average monthly temperatures can result to the attainment of inaccurate results.

The second limitation associated with the collected data in assessing the relative hotness between the selected years is that temperature alone does not provide comprehensive information to determine hotness. This implies that relying on temperature values alone increases the likelihood of inferring inaccurate conclusions when comparing hotness between the selected years. Therefore, a more comprehensive analysis of degree of hotness or coldness requires the integration of other weather data in order to be more accurate. In most cases, there are temperature changes within the annual cycle, implying that the annual average temperature alone does not actually indicate the accurate degree of hotness or coldness. This limitation is worsened by the fact that the data collected can only facilitate a variability analysis basing on the monthly average values. In addition, there are some cases whereby seasons tend to overlap, imposing a further limitation on the seasonal average temperatures. The fundamental argument is that the use of average monthly temperatures only serves to narrow the scope of analysis when determining the relative degree of hotness for the selected years.

4. Explain How Each of the Following could be Applied to your Data and Discuss whether they would Provide any Useful further Insights into your Previous Answers.

- Separate pie chart for each year

A separate pie chart for each year provides a detailed trend analysis for the average monthly temperatures. This will be helpful in a precise analysis of the trends in the monthly average temperatures. The only limitation with having separate pie charts is that its makes it difficult to conduct a comparative study for the selected years. Separate pie charts for each year makes it difficult to compare the two data sets for the two years (Brase 2011). Despite the comparative limitation, having a separate pie chart for each year will make it easy to read the data and facilitate the handling of large data sets. In addition, the visual appealing characteristic of pie charts enhances its readability and thus facilitates the data interpretation. The visual appealing characteristic of pie charts makes it easy to interpret the data. Additionally, separate pie charts for every year eliminates the complexity associated with the integration of both data sets into a single method of presentation. Therefore, having separate pie charts for the two years will help in improving the analysis process conducted above.

- Transformation of the data into a non-linear form.

Variable transformation makes use of mathematical operations in order to adjust the measurement scale. Linear transformation aims at preserving the relationship between the variables. This implies that a correlation between two variables does not change after transforming the data into a linear form. In the case of comparative analysis, transforming data to achieve linearity will not be of useful help because there are no relationships between the variables that are being established, rather, the analysis only aims at assessing the relative degree of hotness between two years. In addition, a linear transformation does not increase or decrease the linear relationship that exists between variables. This is a comparative analysis and not a correlation analysis, implying that there is no need to transform the variables to attain linearity (Johnson & Gouri 2009).

- Computation of the standard deviation of temperature within each month

The standard deviation is a measure dispersion that indicates the degree of dispersion of the data set. If the standard deviation is large, then there are a large range of numbers in the data set. On the other hand, a smaller standard deviation implies that most of the elements in the data set are close to the mean value. The advantage of computing the standard deviation is that it provides a better analysis than when using the mean values alone. The limitation of computing standard deviation is that it is affected by the presence of outliers, which can result to skewed results. Irrespective of the limitation, computing the standard deviation of each data helps in assessing the temperature variability which can be used to infer accurate conclusions regarding the relative degree of hotness in Northern Ireland during 1969 and 1996. Computing the standard deviation for each month will help in increasing the accuracy of the results obtained during the comparative assessment of the degree of hotness in Northern Ireland for the selected years. Therefore, computing the standard deviation of the average monthly temperatures is helpful in providing further insights when comparing the degree of hotness between the selected years.

- Combination with other weather data

Integrating other weather data in the analysis will provide a more comprehensive analysis since there are numerous factors that affect the degree of hotness or coldness. This implies that combining other data such as humidity and precipitation levels will facilitate a more comprehensive and accurate comparative analysis. In this case, combining other weather data is an example of a multivariate data analysis, which facilitates easy visualization and statistical interpretation of the data sets. In addition, combining other weather data means that there is a simultenous analysis of more information resulting in a comprehensive understanding between the various variables affecting the relative degrees of hotness for the selected years. The most important contribution associated with combining all weather data is that the results of analysis are not subject to bias and influence from other factors that have not been taken into consideration. Therefore, combining the data collected with other weather data will help in providing further insights when comparing the relative degree of hotness between the selected months.

5 Discussion on the Relationship between Hotness as Measured in these Statistics, Relative to the Hotness Perceived by People Living in the Area where the Statistics are Calculated

According to the people of Northern Ireland, there are no extremes in temperatures, with the summers being warm and the winters being mild. The lowest temperatures are witnessed in January and February. July is usually the warmest month, with the highest temperature being 30^{o }C. This perceived degrees of hotness by the people of Northern Ireland are consistent with the statistics calculated above. This implies that there is a positive relationship between the computed degree of hotness according to the collected statistics with the perceived degree of hotness by the people of Northern Ireland. The statistics indicates that the degree of hotness in Northern Ireland has increased over the years, which is similar to the views of the people of Northern Ireland who claim that it has become relatively warmer when compared to the past. Northern Ireland is presently characterised by stable temperatures and less variability in monthly temperatures when compared to the past, this indicates that the region has increased its degree of hotness.

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