Question

finish times (to the nearest hour) for 59 dogsled teams are shown below. draw a histogram. use five classes.

261 269 236 244 278 296 284 299 289 289 249 256
338 360 341 333 261 268 287 296 313 311 309 309
299 303 277 283 304 305 288 290 288 289 297 299
332 330 309 327 309 327 285 291 295 298 306 315
310 318 318 320 333 321 323 324 327 239 358

Explanation:

Step1: Find the range

First, find the minimum and maximum values. The minimum value ($\min$) is 236, and the maximum value ($\max$) is 360. The range $R=\max - \min=360 - 236 = 124$.

Step2: Determine class width

We need 5 classes. The class width $w=\lceil\frac{R}{n}
ceil$, where $n = 5$. So $w=\lceil\frac{124}{5}
ceil=\lceil24.8
ceil = 25$.

Step3: Define class intervals

Start with the minimum value. The first class: $236 - 260$ (since $236+25 - 1 = 260$), second: $261 - 285$, third: $286 - 310$, fourth: $311 - 335$, fifth: $336 - 360$.

Step4: Count frequencies

• Class 236 - 260: Values are 236, 244, 249, 256, 239. Frequency ($f$) = 5.
• Class 261 - 285: Values are 261, 269, 278, 261, 268, 277, 283, 285. Frequency ($f$) = 8.
• Class 286 - 310: Values are 284, 289, 289, 287, 296, 309, 309, 299, 303, 304, 305, 288, 290, 288, 289, 297, 299, 309, 309, 291, 295, 298, 306, 310. Frequency ($f$) = 24.
• Class 311 - 335: Values are 313, 311, 327, 327, 315, 318, 318, 320, 321, 323, 324, 327, 332, 330, 333. Frequency ($f$) = 15.
• Class 336 - 360: Values are 338, 360, 341, 333, 358. Frequency ($f$) = 5.

Step5: Draw the histogram

• X - axis: Class intervals (236 - 260, 261 - 285, 286 - 310, 311 - 335, 336 - 360).
• Y - axis: Frequency.
• For each class, draw a bar with height equal to its frequency.

Answer:

The histogram has 5 classes with intervals 236 - 260 (frequency 5), 261 - 285 (frequency 8), 286 - 310 (frequency 24), 311 - 335 (frequency 15), 336 - 360 (frequency 5). The bars are drawn with heights corresponding to these frequencies on the y - axis and class intervals on the x - axis.