Q. 53 - The Practice of Statistics for AP

Question

Exercises 53 and 54 refer to the following setting. The table below displays the number of accidents at a factory during each hour of a 24-hour shift (1  1 a.m).

53. Accidents happen (1.2, 3.1)
(a) Construct a plot that displays the distribution of the number of accidents effectively.
(b) Construct a plot that shows the relationship between the number of accidents and the time when they occurred.
(c) Describe something that the plot in part (a) tells you about the data that the plot in part (b) does not.
(d) Describe something that the plot in part (b) tells you about the data that the plot in part (a) does not.

Step-by-Step Solution

Answer

(a) Constructed a plot that displays the distribution of the number of accidents effectively as:

(b) Constructed a plot that shows the relationship between the number of accidents and the time when they occurred as:

(c) The plot created in section (b) does not reveal that the distribution is skewed to the left, as the histogram constructed in part (a) does (b).
(d) The number of accidents is largest at hours $5, 13,$ and $21,$ according to the plot generated in part (b), which is not indicated by the histogram constructed in part (a).

Part (a) Step 1: Given information

To construct a plot that displays the distribution of the number of accidents effectively with given data.

Hour	Number of accidents
1	5
2	8
3	17
4	31
5	24
6	18
7	12
8	7
9	1
10	0
11	2
12	14
13	21
14	12
15	10
16	1
17	0
18	1
19	3
20	21
21	23
22	18
23	11
24	2

Part (a) Step 1: Explanation

Plot that displays the distribution of the number of accidents effectively with given data as follows:

Part (b) Step 1: Given information

To construct a plot that shows the relationship between the number of accidents and the time.

Part (b) Step 2: Explanation

Plot all of the given data points on a scatter plot and connect each one to an hour later as:

Part (c) Step 1: Given information

To describe the plot in part (a) tells about the data that the plot in part (b) does not.

Part (c) Step 2: Explanation

Plot from part (a):

Part (c) Step 3: Explanation

Plot from part (b):

The plot created in section (b) does not reveal that the distribution is skewed to the left, as the histogram constructed in part (a) does (b).

Part (d) Step 1: Given information

To describe the plot in part (b) tells you about the data that the plot in part (a) does not.

Part (d) Step 2: Explanation

Plot from part (a):

Part (d) Step 3: Explanation

Plot from part (b):

The number of accidents is largest at hours $5, 13,$ and $21$, according to the plot generated in part (b), which is not indicated by the histogram constructed in part (a).