Answer:
Explanation:
To construct a frequency distribution and a frequency histogram for the given data set, we need to divide the range of the data into a specified number of classes. In this case, the number of classes is 8.
To start, we need to determine the range of the data. The highest value in the data set is 514, and the lowest value is 292. So, the range is 514 - 292 = 222.
Next, we need to determine the width of each class. To do this, we divide the range by the number of classes: 222 / 8 = 27.75. Since it is not practical to have a fraction as a class width, we can round it up to the nearest whole number. So, the class width is 28.
Now, let's construct the frequency distribution table. We start with the minimum data entry, which is 292, and use the class width of 28 to determine the upper limits of each class.
Class 1: 292 - 319
Class 2: 320 - 347
Class 3: 348 - 375
Class 4: 376 - 403
Class 5: 404 - 431
Class 6: 432 - 459
Class 7: 460 - 487
Class 8: 488 - 515
Now, we count the number of data values that fall into each class. Let's fill in the frequency column of the frequency distribution table:
Class 1: 292 - 319 (frequency = 2)
Class 2: 320 - 347 (frequency = 3)
Class 3: 348 - 375 (frequency = 4)
Class 4: 376 - 403 (frequency = 5)
Class 5: 404 - 431 (frequency = 5)
Class 6: 432 - 459 (frequency = 4)
Class 7: 460 - 487 (frequency = 2)
Class 8: 488 - 515 (frequency = 5)
Now that we have the frequency distribution, we can construct the frequency histogram. The x-axis represents the classes, and the y-axis represents the frequency. We can use rectangles to represent each class and its corresponding frequency. The height of each rectangle represents the frequency, and the width represents the class width.
By looking at the frequency histogram, we can observe patterns or trends in the data. For example, we can see that the most common reaction time falls into the fourth class, which is 376 - 403 milliseconds. Additionally, there is a relatively higher frequency in the fifth and eighth classes compared to other classes.
In summary, the frequency distribution and frequency histogram provide a visual representation of the data set. The frequency distribution helps organize the data into classes, while the frequency histogram gives a graphical representation of the distribution of reaction times.