Question

Major World Lakes A lake is a body of water surrounded by land. Hence, some bodies of water named "seas," like the Caspian Sea, are actual salt lakes. In the table that follows, the length in miles is listed for the major natural lakes of the world, excluding the Caspian Sea, which has a length of 760 miles \({ }^{5}\) $$\begin{array}{lclc}\text { Name } & \text { Length (mi) } & \text { Name } & \text { Length (mi) } \\\\\hline \text { Superior } & 350 & \text { Titicaca } & 122 \\\\\text { Victoria } & 250 & \text { Nicaragua } & 102 \\\\\text { Huron } & 206 & \text { Athabasca } & 208 \\\\\text { Michigan } & 307 & \text { Reindeer } & 143 \\\\\text { Aral Sea } & 260 & \text { Tonle Sap } & 70 \\\\\text { Tanganyika } & 420 & \text { Turkana } & 154\end{array}$$ $$\begin{array}{lllr}\text { Baykal } & 395 & \text { Issyk Kul } & 115 \\\\\text { Great Bear } & 192 & \text { Torrens } & 130 \\\\\text { Nyasa } & 360 & \text { Vãnern } & 91 \\\\\text { Great Slave } & 298 & \text { Nettilling } & 67 \\\\\text { Erie } & 241 & \text { Winnipegosis } & 141 \\\\\text { Winnipeg } & 266 & \text { Albert } & 100 \\\\\text { Ontario } & 193 & \text { Nipigon } & 72 \\\\\text { Balkhash } & 376 & \text { Gairdner } & 90 \\\\\text { Ladoga } & 124 & \text { Urmia } & 90 \\\\\text { Maracaibo } & 133 & \text { Manitoba } & 140 \\\\\text { Onega } & 145 & \text { Chad } & 175 \\\\\text { Eyre } & 90 & &\end{array}$$ a. Use a stem and leaf plot to describe the lengths of the world's major lakes. b. Use a histogram to display these same data. How does this compare to the stem and leaf plot in part a? c. Are these data symmetric or skewed? If skewed, what is the direction of the skewing?

Short answer

If skewed, in which direction? Answer: The distribution of the data is positively skewed, with the tail extending to the right (larger values).

Step-by-step solution

(Step 1: Create a stem and leaf plot)

To create a stem and leaf plot, we need to follow these steps: - Round the given lengths to the nearest ten. - Group the rounded lengths by the tens digit (stem) and list the ones digit (leaf) next to the stem. Stem and leaf plot: ``` 6|7 7|011111111111233334444444455555 8|013333445555666778888888888889 9|111111111388 10|0337 11|0323479 12|2558 ```

(Step 2: Create a histogram and compare it to the stem and leaf plot)

To create a histogram, we need to follow these steps: - Divide the data into intervals, usually of equal width. - Count the number of data points in each interval. - Draw a bar for each interval that corresponds to the count of data points within that interval. The histogram is as follows (using intervals of 50): ``` 50 - 99: ******* 100 - 149: ************ 150 - 199: ************ 200 - 249: ******* 250 - 299: ********* 300 - 349: ** 350 - 399: **** ``` Comparison between stem and leaf plot and histogram: - Stem and leaf plot retains the original data, while the histogram displays frequencies in intervals. - Both plots show the general distribution of data points.

(Step 3: Determine if the data is symmetric or skewed)

By observing the stem and leaf plot and the histogram, the data seems to be positively skewed. This means that the majority of the data points are concentrated on the lower end of the scale, and the tail extends to the right (larger values).