Question

7. The following is the number of passengers per ight in a sample of 34 ights
from Ottawa, Ontario, to Hampton, Washington in 2018.
78 73 75 99 50 58 25 56 57 55 59 55 62 69 77 66 51
21 53 30 51 63 52 57 68 75 66 65 69 79 72 65 53 50

(a) What is the population under consideration here? What is the used
measurement unit?

(b) What is the variable of interest here? Is it quantitative and continuous,
or quantitative and discrete?

(c) Thirty percent of ights have passengers exceeding what value?

(d) Draw a stem-and-leaf plot with stems 1, 2, 3... . What is the leaf unit?

(e) Describe the shape of the data set.

(f) Find the percentage of measurements falling in the intervals xks for k =
1; 2; 3.

(g) How do you compare the percentages obtained in part (f) with those
given by the Empirical Rule? Explain.

Answer 1

dear student, we can provide you with solution of four sub question at a time.

a) the population under consideration is the passenger travelling in flight from Ontario to Hampton

b) Variable of interest here is the number of passengers in the flight. This variable is discrete and quantitative.

c) Here we have to find the 30th percentile.

1	21
2	25
3	30
4	50
5	50
6	51
7	51
8	52
9	53
10	53
11	55
12	55
13	56
14	57
15	57
16	58
17	59
18	62
19	63
20	65
21	65
22	66
23	66
24	68
25	69
26	69
27	72
28	73
29	75
30	75
31	77
32	78
33	79
34	99

The next step is to compute the position (or rank) of the 30% percentile. The following is obtained:

Percentile Position =

Since the position found is not integer, the method of interpolation needs to be used. The 30% percentile is located between the values in the positions 10 and 11. Those values, based on the data organised in ascending order, are 53 and 55.

The value of 10.5 - 10 = 0.5 corresponds to the proportion of the distance between 53 and 55 where the percentile we are looking for is located at. In fact, we compute

This completes the calculation.

d)