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== 16.4#h(0.6em)Statistical Literacy


    #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[
#emph[Prerequisites]


      Log #linebreak() 
                 #linebreak()
]


    Many financial web pages give you the option of using a linear or a logarithmic Y-axis. An example from Google Finance is shown below.


    #figure(figph[Screenshot of an online stock-chart tool showing a market index from October 2002 to September 2012 on a Linear vertical scale (the Logarithmic option is unselected beneath the chart). The shaded line climbs from about 9,500 in 2004 to a peak near 14,000 in 2007, plunges to about 6,600 in early 2009, then recovers to roughly 13,500 by 2012; the header reads +5780.14 (75.05%).], alt: "Screenshot of an online stock-chart tool showing a market index from October 2002 to September 2012 on a Linear vertical scale (the Logarithmic option is unselected beneath the chart). The shaded line climbs from about 9,500 in 2004 to a peak near 14,000 in 2007, plunges to about 6,600 in early 2009, then recovers to roughly 13,500 by 2012; the header reads +5780.14 (75.05%).", caption: none)


    
=== What do you think?


    To get a straight line with the linear option chosen, the price would have to go up the same amount every time period. What would result in a straight line with the logarithmic option chosen?


    The price would have to go up the same proportion every time period. For example, go up 0.1% every day.


    Housing Appreciation


    The graph at the top of #link("http://www.forecast-chart.com/estate-real-miami.html")[this page]  states that the prices are shown in a logarithmic scale.


    
=== What do you think?


    The Y-axis values do not appear to be a log scale. Interpret the scale for the Y-axis.


    Note that the distance between 10 and 100 is the same as the distance between 100 and 1,000. That makes it a log scale since equal proportional increases are represented by the same difference on the graph. For ease of interpretation, the log values are translated back to raw scores for the labels.