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

The histogram for the data is attached below.

Step-by-step 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:

Compute the class width:

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.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

my answer got deleted but it's a

step-by-step explanation: