Question

The data shown are cigarette taxes per pack in cents imposed by each state (and DC and US territories) as of December 2018.  

68	200	200	115	287	84	435	210	450	134
37	320	57	198	100	136	129	110	108	200
200	351	200	304	68	17	170	64	180	178
270	166	435	45	44	160	203	133	260	57
153	62	141	170	308	30	303	120	252	60
509	400	375	425

Source: https://www.tobaccofreekids.org/assets/factsheets/0097.pdf

9.         Construct a frequency distribution using six classes.

10.       There are several different ways to picture data.  What way do you think would be the most effective for these data? Explain the reason for your answer.

11.       What will the MEAN of the data tell us?  What is the mean of these data?

12.       What will the MODE of the data tell us?  What is the mode of these data?

13.       What will the Median of the data tell us?  What is the median of these data?  

14.       Explain which of the measures you found above is the most meaningful for this data set?  

15.       Which of these taxes fall in the 90^th– 99^thpercentiles?

Answer 1

9) The given data is 68,200,200,115,287,84,435,210,450,134,37,320,57,198,100,136,129,110,108,200,200,351,200,304,68,17,170,64,180,178,270,166,435,45,44,160,203,133,260,57,153,62,141,170,308,30,303,120,252,60,509,400,375,425

Arrange the given data into a frequency table by taking 6 classes with width of 83

Class frequency(f) midpoint(x) f. X cf

17-100 14 58.5 819 14

100-183 16 141.5 2264 30

183-266 10 224.5 2245 40

266-349 6 307.5 1845 46

349-432 4 390.5 1562 50

432-515 4 473.5 1894 54

11) mean =sum(fx) /N

where N=54

Mean= 10629/54

Mean= 196.8333

Mean showing that it is extremely effected it is so far to some observations. So it may not be best measure for given data

12) mode= L + ( f-f1/2f-f1-f2 ) C

L= lower limit of mode clss

f = frequency of mode clss

f1=previous clss frequency of mode class

f2=after class frequency of mode class

Mode = 100+(16-14) 100/32-14-10

Mode = 120.75

13) median =L +( N/2 -cf / F) 100

Median = 100 + ( 27-14/16) 100

Median = 167.4375

Finally we conclude that arithmetic mean is best measure for given data because mean >median >mode