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• Temperature anomalies


  Differences from the average temperature from 1951 to 1980
• Plotting line charts


  1. Download data

  2. Understand how temperature is measured

  3. Create line charts using monthly, seasonal, and annual data

  4. Identify patterns over time
• If you add up marginal utility for each unit you get total utility
• Frequency table


  • A record of how many observations in a dataset have a particular value, range of values, or belong to a particular category
• Creating a frequency table

  1. Create a table

  2. Filter the data

  3. Use the FREQUENCY function to fill in the rest of the table
• Frequency tables


  • Figure 1.5
  • Figure 1.6
• Plotting column charts


  Plot two separate column charts for 1951–1980 and 1981–2010 to show the distribution of temperatures
• The New York Times article uses the same temperature dataset to investigate the distribution of temperatures and temperature variability over time
• The government is worried that climate change will result in more frequent extreme weather events
• The island has experienced a few major storms and severe heat waves in the past, both of which caused serious damage and disruption to economic activity
• The government is concerned about whether weather will become more extreme and vary more as a result of climate change
• ill use Excel's FREQUENCY function to fill in Column B. First, select the cells that need to be filled in.
• Use the FREQUENCY function to fill in the rest of the table


  Excel will fill in the frequency table based on the values in the cells selected
• The values you get will be slightly different to those shown here, because this station temperature data is slightly different.
• Figure 1.6 How to create a frequency table in Excel.
• Using the frequency tables from Question 1: Plot two separate column charts for 1951–1980 and 1981–2010 to show the distribution of temperatures, with frequency on the vertical axis and the range of temperature anomaly on the horizontal axis. Your charts should look similar to those in the New York Times article.
• Using your charts, describe the similarities and differences (if any) between the distributions of temperature anomalies in 1951–1980 and 1981–2010.
• variance


  A measure of dispersion in a frequency distribution, equal to the mean of the squares of the deviations from the arithmetic mean of the distribution. The variance is used to indicate how 'spread out' the data is. A higher variance means that the data is more spread out.
• Example

  • The set of numbers 1, 1, 1 has zero variance (no variation), while the set of numbers 1, 1, 999 has a high variance of 221,334 (large spread).
• Now we will use our data to look at different aspects of distributions. First, we will learn how to use deciles to determine which observations are 'normal' and 'abnormal', and then learn how to use variance to describe the shape of a distribution.
• The New York Times article considers the bottom third (the lowest or coldest one-third) of temperature anomalies in 1951–1980 as 'cold' and the top third (the highest or hottest one-third) of anomalies as 'hot'. In decile terms, temperatures in the 1st to 3rd decile are 'cold' and temperatures in the 7th to 10th decile or above are 'hot' (rounded to the nearest decile).
• Figure 1.7 How to use Excel's PERCENTILE.INC function.
• Does your answer suggest that we are experiencing hotter weather more frequently in 1981–2010? (Remember that each decile represents 10% of observations, so 30% of temperatures were considered 'hot' in 1951–1980.)
• Figure 1.8 How to use Excel's COUNTIF function.
• Figure 1.9 How to calculate variance.
• Using the findings of the New York Times article and your answers to Questions 1 to 5, discuss whether temperature appears to be more variable over time. Would you advise the government to spend more money on mitigating the effects of extreme weather events?
• correlation


  A measure of how closely related two variables are. Two variables are correlated if knowing the value of one variable provides information on the likely value of the other, for example high values of one variable being commonly observed along with high values of the other variable. Correlation can be positive or negative. It is negative when high values of one variable are observed with low values of the other. Correlation does not mean that there is a causal relationship between the variables.
• Example


  • When the weather is hotter, purchases of ice cream are higher. Temperature and ice cream sales are positively correlated. On the other hand, if purchases of hot beverages decrease when the weather is hotter, we say that temperature and hot beverage sales are negatively correlated.
• correlation coefficient


  A numerical measure, ranging between 1 and −1, of how closely associated two variables are—whether they tend to rise and fall together, or move in opposite directions. A positive coefficient indicates that when one variable takes a high (low) value, the other tends to be high (low) too, and a negative coefficient indicates that when one variable is high the other is likely to be low. A value of 1 or −1 indicates that knowing the value of one of the variables would allow you to perfectly predict the value of the other. A value of 0 indicates that knowing one of the variables provides no information about the value of the other.
• The government has heard that carbon emissions could be responsible for climate change, and has asked you to investigate whether this is the case. To do so, we are now going to look at carbon emissions over time, and use another type of chart (scatter charts) to show their relationship with temperature anomalies.
• In the questions below, we will make charts using the CO2 data from the US National Oceanic and Atmospheric Administration. Download the Excel spreadsheet containing this data.
• trend


  Similar to, but not identical to, the 'interpolated' measure of CO2 levels. Explain the difference between these two measures and why there might be seasonal variation in CO2 levels.
• Discuss the shortcomings of using this coefficient to summarize the relationship between variables.
• Figure 1.10 How to calculate correlation and draw a scatterplot.
• Correlation coefficient

  Measure of the strength of the linear relationship between two variables, ranging from -1 to 1
• A correlation coefficient of 1 or -1 means there is a perfect upward- or downward-sloping linear relationship between the two variables
• A correlation coefficient of 0 means there is no systematic upward- or downward-sloping linear relationship between the two variables
• The correlation coefficient only tells us about the strength of the linear relationship between two variables
• The correlation coefficient cannot detect non-linear relationships (e.g. a U-shaped pattern)