Question

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

Number of​ classes: 8

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

430 386 352 301 450 291 429 467 454 385 380
373 386 307 321 336 310 413 306 357 514 443
442 326 508 424 386 429 412 418

Answer 1

The histogram for the data is attached below.

Explanation:

Arrange the data in ascending order as follows:

S = {291 , 301 , 306 , 307 , 310 , 321 , 326 , 336 , 352 , 357 , 373 , 380 , 385 , 386 , 386 , 386 , 412 , 413 , 418 , 424 , 429 , 429 , 430 , 442 , 443 , 450 , 454 , 467 , 508 , 514}

Compute the range:

`Range=Max.-Min.\\=514-291\\=223`

Compute the class width:

`Class\ Width =(Range)/(No.\ of\ classes)=(223)/(8)=27.875\approx 28`

The classes are as follows:

290 - 318

319 - 347

348 - 376

377 - 405

406 - 434

435 - 463

464 - 492

493 - 521

Compute the frequency distribution as follows:

Class Interval Frequency

290 - 318 5

319 - 347 3

348 - 376 3

377 - 405 5

406 - 434 7

435 - 463 4

464 - 492 1

493 - 521 2

The histogram for the data is attached below.