EXAMPLE 4 Lake elevation levels

Lake Murray is a manmade reservoir located in South Carolina. It is used mainly for recreation, such as boating, fishing, and water sports. It is also used to provide backup hydroelectric power for South Carolina Electric and Gas. The lake levels fluctuate with the highest levels in summer (for safe boating and good fishing) and the lowest levels in winter (for water quality). Water can be released at the dam in the case of heavy rains or to let water out to maintain winter levels. The U.S. Geological Survey (USGS) monitors water levels in Lake Murray. The histograms in Figure 11.3 were created using 67,810 hourly elevation levels from November 1, 2007, through August 11, 2015.

The two histograms of lake levels were made from the same data set, and the histograms look identical in shape. The shape of the distribution of lake levels is skewed left because the left side of the histogram is longer. The minimum lake level is 350 feet, and the maximum is 359 feet. Using the histogram on the right, by adding the height of the bar for 358 and 359 feet elevations, we see the lake level is at 358 or 359 roughly 40% of the time. Using this information, it appears that a lake level of 357 feet is the midpoint of the distribution.

Let’s examine the difference in the two histograms. The histogram on the left puts the count of observations on the vertical axis (this is called a frequency histogram), while the histogram on the right uses the percentage of times the lake reaches a certain level (this is called a relative frequency histogram). The frequency histogram tells us the lake reached an elevation of 358 feet approximately 24,000 times (24,041, to be exact!). If a fisherman considering a move to Lake Murray cares about how often the lake reaches a certain level, it is more illustrative to use the relative frequency histogram on the right, which reports the percentage of times the lake reached 358 feet. The height of the bar for 358 feet is 35, so the fisherman would know the lake is at the 358 foot elevation roughly 35% of the time.