Finish times (to the nearest hour) for 59 dogsled teams are shown below. Draw a histogram. Use five classes.
261
269
236
244
280
296
284
297
290
290
247
256
338
360
341
333
261
267
287
296
313
311
309
309
299
303
277
283
304
305
286
290
286
287
297
299
332
330
309
326
309
326
285
291
295
298
306
315
310
318
318
320
333
321
323
324
327
239
358
The frequency table for the above data is given below.
Class Limits
Boundaries
Midpoint
Freq.
Relative Freq.
Cumulative Freq.
236 260
235.5 260.5
248
5
0.08
5
261 285
260.5 285.5
273
9
0.15
14
286 310
285.5 310.5
298
25
0.42
39
311 335
310.5 335.5
323
16
0.27
55
336 360
335.5 360.5
348
4
0.07
59
We can't draw histograms in this forum.
24
To create a histogram, we need to plot the class boundaries on the x-axis and the frequency on the y-axis. Each class will be represented by a bar whose height corresponds to its frequency.
Using the frequency table provided, we can draw the histogram as follows:
Class Limits:
236-260, 261-285, 286-310, 311-335, 336-360
(Note: The class limits are the first and last values of each class.)
Boundaries:
235.5-260.5, 260.5-285.5, 285.5-310.5, 310.5-335.5, 335.5-360.5
(Note: The boundaries are the midpoints between the class limits.)
Midpoint:
248, 273, 298, 323, 348
(Note: The midpoint is the average of the lower and upper class limits.)
Frequency:
5, 9, 25, 16, 4
Now, let's plot these values on a graph:
_____________________
| * |
| * |
| * * * |
| * |
|____*____|
X-Axis: Class Boundaries
Y-Axis: Frequency
Legend:
* Represents the frequency value for each class
Frequencies:
5 for the first class, 9 for the second class, 25 for the third class, 16 for the fourth class, and 4 for the fifth class.
The histogram now represents the distribution of finish times for the 59 dogsled teams.
To create a histogram for the given data, follow these steps:
1. Determine the range of the data: Subtract the smallest value from the largest value. In this case, the range is 360 - 236 = 124.
2. Decide on the number of classes: In this case, the question specifies using five classes.
3. Calculate the class width: Divide the range by the number of classes (rounded up if needed) to determine the width of each class. In this case, the class width is 124 / 5 = 24.8. Round this up to 25 to get a whole number.
4. Determine the class boundaries: Start with the smallest value and add the class width to create the boundaries for each class. Using the given data, the class boundaries are:
- Class 1: 236 - 260
- Class 2: 261 - 285
- Class 3: 286 - 310
- Class 4: 311 - 335
- Class 5: 336 - 360
5. Count the frequency of values within each class: Count how many values from the given data fall within each class range. Record these frequencies in the frequency column of the frequency table.
6. Calculate the relative frequency: Divide each frequency by the total number of data points (59 in this case). Record these relative frequencies in the relative frequency column of the frequency table.
7. Calculate the cumulative frequency: Sum up the frequencies as you move down the table. Record these cumulative frequencies in the cumulative frequency column of the frequency table.
8. Create the histogram: On a graph paper or computer software, create a horizontal axis labeled with the class boundaries. On the vertical axis, label it with the frequency.
9. Draw a bar for each class: For each class, draw a rectangle/bar whose height corresponds to the frequency in that class. The width of each bar should be proportional to the class width, and the bars should be next to each other on the horizontal axis.
10. Optional: Add labels and a title to the histogram to make it clear and informative.
That's it! You have now created a histogram for the given data.