Question

A manager at an amusement park wants to know how popular the park's biggest roller coaster is. She counts the number of people waiting in line every half hour. The results are shown below.
19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,36,37



Plot the values that represent the minimum, maximum, first quartile, median, and third quartile of the number of people waiting in line.




Plz help i have alot of trouble finding the quartials

Answer 1

Answer: minimum = 0.5

maximum = 9.0

first quartile = 3

median = 5.5

third quartile = 7.5

Step-by-step explanation:

The histogram is shown below and used to obtain the various information

Time (hour) (X)     No of People (F)       FX

0.5                             19                            9.5  -- minimum = 0.5    

1                                20                            20

1.5                              21                             31.5

2                                 22                            44

2.5                              23                            57.5

3                                 24                             72 ----first quartile = 3

3.5                              26                             91

4                                 27                              108

4.5                             28                               126

5                                29                                145

5.5                            30                               165 --median/ inter quartile =5.5

6                               31                                186

6.5                           32                                208

7                               33                                 231

7.5                            34                                255-- third quartile = 7.5

8                               35                                280

8.5                            36                               306        

9                                37                              333 --- maximum = 9

T=85.5                   T = 507                      T=  2666.82     T = TOTAL

mean = sumFX/sumF  =   2666.82/507 = 5.26

Median = middle number = inter quartile =5.5 (507/2 = 253.5 = 254 and  add the frequency from top = 19+20+21+ 22+ 23+ 24+26+ 27+ 28+ 29 =269

and 254  close to 269 that is the frequency is within the range and corresponds to 5.5

first quartile = 1/4 *507 = 126.75 = 127 ( add the frequency from top= 19+20+21+ 22+ 23+ 24= 129 and 127 is close to 129)

third quartile = 3/4 * 507 = 380.25 ( add the frequency from top = 19+20+21+ 22+ 23+ 24+26+ 27+ 28+ 29+ 30+ 31+32+ 33+ 34 = 399 and 380 is close to 399 so the third quartile is 7.5

minimum is the one with lowest frequency = 0.5 at 19

maximum  or mode is the one with highest frequency = 9 at 37