Construct a frequency distribution and a frequency histogram for the data set using the indicated number of classes. Describe any patterns.

Question

Number of​ classes: 8

Data​ set: Reaction times​ (in milliseconds) of 30 adult females to an auditory stimulus

428 293 382 338 514 423

389 426 372 313 442 386

352 470 389 412 444 425

303 455 306 306 322 414

450 387 320 357 508 418

Find the Class and Frequency

1. ____ -_____ _____
2. ____ - _____ ______
3. ____ - _____ ______
4. ____ - _____ ______
5. ____- _____ ______
6. ____ - _____ _____
7. ____ - _____ ______

Answer 1

It's a bit confusing because you list 7 classes but the directions say 8 classes.

If there are 7 classes, I would subtract 1 from the lowest number and add one to the highest number to get an even number for each class (with a class width of 31):

Low High

Limit Limit Frequency

292 323 7

324 355 2

356 387 5

388 419 5

420 451 7

452 483 2

484 515 2

If there were 8 classes, I would also subtract one from the lowest and add one to the largest and then use a class width of 27:

Low High

Limit Limit Frequency

292 319 5

320 347 3

348 375 3

376 403 5

404 431 7

432 459 4

460 487 1

488 515 2

Looking at the respective charts, it appears the data is bimodal.

Answer 2

Since there are 7 classes, we may use each (100/7)~14.5th percentiles as cutting point to construct bins. First sort the values from smallest to largest. Then calculate the lower and upper values for the first 14.5th percentile (the upper value is a number for which approximately 14.5% of the sorted data is smaller or equal to, in this case 314.5), then continue doing this for the second bucket (numbers that fall in the range of 14.5% and 29% of sorted data) and continue the process. The percentiles can be calculated using Excel or any other statistical software. The buckets are obtained are as follows which shows a relatively uniform distribution.