Data summaries

Basic graphical representations of data as used in the ozone lab

There are different ways how to plot data

• time series - entire time period vs. just the hours
• bar graph vs. line plot (example: precipitation)
• cyclicity, period
• make the graph long, focus on a few days of data at the time
• histograms
• bins, frequency (array formula!), radar diagram
• example: income in US
• scatter plots
• correlations

Descriptive statistics (qualitative, we will discuss the details later)

• count
• how many numbers are
• average (arithmetic mean)
• the mean is the sum of a set of numbers divided by how many there are.
• median
• the median is the number in the middle of a set of numbers; that is, half the numbers have values that are greater than the median, and half have values that are less.
• mode
• the mode is  the most frequently occurring, or repetitive, value in an array or range of data.
• minimum
• maximum
• range
• maximum - minimum
• standard deviation
• the standard deviation is a measure of how widely values are dispersed from the average value (the mean).
• variance
• another measure of the spread of the data.
• kurtosis
• kurtosis characterizes the relative peakedness or flatness of a distribution compared with the normal distribution. Positive kurtosis indicates a relatively peaked distribution. Negative kurtosis indicates a relatively flat distribution.
• skewness
• skewness characterizes the degree of asymmetry of a distribution around its mean. Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values. Negative skewness indicates a distribution with an asymmetric tail extending toward more negative values.