How long does it take to finish the 1161 -mile Iditarod Dog...

How long does it take to finish the 1161 -mile Iditarod Dog Sled Race from Anchorage to Nome, Alaska (see Viewpoint)? Finish times (to the nearest hour) for 57 dogsled teams are shown below. $$\begin{aligned} &\begin{array}{rrrrrrrrrrr} 261 & 271 & 236 & 244 & 279 & 296 & 284 & 299 & 288 & 288 & 247 & 256 \end{array}\\ &\begin{array}{rrrrrrrrrr} 338 & 360 & 341 & 333 & 261 & 266 & 287 & 296 & 313 & 311 & 307 & 307 \end{array}\\ &\begin{array}{cccccccccccc} 299 & 303 & 277 & 283 & 304 & 305 & 288 & 290 & 288 & 289 & 297 & 299 \end{array}\\ &\begin{array}{rrrrrrrrrr} 332 & 330 & 309 & 328 & 307 & 328 & 285 & 291 & 295 & 298 & 306 & 315 \end{array}\\ &\begin{array}{rrrrrrr} 310 & 318 & 318 & 320 & 333 & 321 & 323 & 324 & 327 \end{array} \end{aligned}$$ Use five classes.

How long does it take to finish the 1161 -mile Iditarod Dog Sled Race from Anchorage to Nome, Alaska (see Viewpoint)? Finish times (to the nearest hour) for 57 dogsled teams are shown below.
$$\begin{aligned}
&\begin{array}{rrrrrrrrrrr}
261 & 271 & 236 & 244 & 279 & 296 & 284 & 299 & 288 & 288 & 247 & 256
\end{array}\\
&\begin{array}{rrrrrrrrrr}
338 & 360 & 341 & 333 & 261 & 266 & 287 & 296 & 313 & 311 & 307 & 307
\end{array}\\
&\begin{array}{cccccccccccc}
299 & 303 & 277 & 283 & 304 & 305 & 288 & 290 & 288 & 289 & 297 & 299
\end{array}\\
&\begin{array}{rrrrrrrrrr}
332 & 330 & 309 & 328 & 307 & 328 & 285 & 291 & 295 & 298 & 306 & 315
\end{array}\\
&\begin{array}{rrrrrrr}
310 & 318 & 318 & 320 & 333 & 321 & 323 & 324 & 327
\end{array}
\end{aligned}$$
Use five classes.

Key Concepts

Frequency Distribution

A frequency distribution is a summary of how often each value or range of values occurs in a dataset. It helps organize data by categorizing it into classes and counting the number of observations in each class, which is essential for understanding the overall pattern of the data.

Histogram

A histogram is a graphical representation of the frequency distribution of a dataset. It uses bars to depict the frequency of data points within designated class intervals, allowing for a visual assessment of the distribution shape, spread, and central tendency.

Class Interval

A class interval, or class, is a range of values into which data is grouped in a frequency distribution. Defining appropriate class intervals is crucial for summarizing data effectively, as it directly influences the interpretation of the distribution and subsequent analyses such as constructing histograms.

Range

The range is a measure of dispersion that represents the difference between the maximum and minimum values in a dataset. It provides a simple sense of how spread out the data are and is used to help determine suitable class intervals when grouping data.

Class Width

Class width is the size of each class interval in a frequency distribution and is calculated by dividing the range of the data by the number of classes. It determines the span that each class covers and is critical for ensuring that the data is evenly and appropriately segmented for analysis.

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