A transportation researcher decided to record the number of miles that employees of a large company drove to work each day. The frequency table below displays the data. Which histogram represents the data?
# of miles
Tally
Frequency
0–5
|||
3
6–10
|||| |||
8
11–15
|||| |||
8
16–20
|||| |||
8
21–25
||||
5
26–30
|||
3
A. A histogram is shown.The horizontal axis is labeled # of Miles. It is divided into six partitions. The first partition extends from 0 to 5 on the x-axis. The second partition extends from 5 to 10 on the x-axis. The third partition extends from 10 to 15 on the x-axis. The fourth partition extends from 15 to 20 on the x-axis. The fifth partition extends from 20 to 25 on the x-axis. The sixth partition extends from 25 to 30 on the x-axis. The vertical axis is labeled Frequency. It is numbered from 0 to 8 with a step size of 2. Six rectangles or bars are shown. The rectangle spanning the 0 to 5 partition has a height of 3. The rectangle spanning the 5 to 10 partition has a height of 8. The rectangle spanning the 10 to 15 partition has a height of 8. The rectangle spanning the 15 to 20 partition has a height of 8. The rectangle spanning the 20 to 25 partition has a height of 5. The rectangle spanning the 25 to 30 partition has a height of 3.
B. A histogram is shown.The horizontal axis is labeled # of Miles. It is divided into six partitions. The first partition extends from 0 to 5 on the x-axis. The second partition extends from 5 to 10 on the x-axis. The third partition extends from 10 to 15 on the x-axis. The fourth partition extends from 15 to 20 on the x-axis. The fifth partition extends from 20 to 25 on the x-axis. The sixth partition extends from 25 to 30 on the x-axis. The vertical axis is labeled Frequency. It is numbered from 0 to 8 with a step size of 2. Six rectangles or bars are shown. The rectangle spanning the 0 to 5 partition has a height of 2. The rectangle spanning the 5 to 10 partition has a height of 8. The rectangle spanning the 10 to 15 partition has a height of 8. The rectangle spanning the 15 to 20 partition has a height of 4. The rectangle spanning the 20 to 25 partition has a height of 5. The rectangle spanning the 25 to 30 partition has a height of 3.
C. A histogram is shown.The horizontal axis is labeled # of Miles. It is divided into five partitions. The first partition extends from 5 to 10 on the x-axis. The second partition extends from 10 to 15 on the x-axis. The third partition extends from 15 to 20 on the x-axis. The fourth partition extends from 20 to 25 on the x-axis. The fifth partition extends from 25 to 30 on the x-axis. The vertical axis is labeled Frequency. It is numbered from 0 to 8 with a step size of 2. Five rectangles or bars are shown. The rectangle spanning the 5 to 10 partition has a height of 5. The rectangle spanning the 10 to 15 partition has a height of 8. The rectangle spanning the 15 to 20 partition has a height of 4. The rectangle spanning the 20 to 25 partition has a height of 5. The rectangle spanning the 25 to 30 partition has a height of 3.
D. A histogram is shown.
B. A histogram is shown. The horizontal axis is labeled # of Miles. It is divided into six partitions. The first partition extends from 0 to 5 on the x-axis. The second partition extends from 5 to 10 on the x-axis. The third partition extends from 10 to 15 on the x-axis. The fourth partition extends from 15 to 20 on the x-axis. The fifth partition extends from 20 to 25 on the x-axis. The sixth partition extends from 25 to 30 on the x-axis. The vertical axis is labeled Frequency. It is numbered from 0 to 8 with a step size of 2. Six rectangles or bars are shown. The rectangle spanning the 0 to 5 partition has a height of 2. The rectangle spanning the 5 to 10 partition has a height of 8. The rectangle spanning the 10 to 15 partition has a height of 8. The rectangle spanning the 15 to 20 partition has a height of 4. The rectangle spanning the 20 to 25 partition has a height of 5. The rectangle spanning the 25 to 30 partition has a height of 3.
The table shows Christine’s best javelin throws each year. Make a scatter plot that represents the given data.
Year
1997
1998
1999
2000
2001
2002
2003
2004
Distance (m)
39.75
41.25
40.25
40.5
43.5
43.5
41.5
45.75
A.
distance graph
The x-axis shows numbers from 1997 to 2004 with a step size of 1. It is labeled Year, The y-axis shows numbers from 39 to 46 with a step size of 1. It is labeled Distance (m), The points shown are approximately left-parenthesis 1997 comma 39.8 right-parenthesis, left-parenthesis 1998 comma 40.2 right-parenthesis, left-parenthesis 1999 comma 40.5 right-parenthesis, left-parenthesis 2000 comma 41.4 right-parenthesis, left-parenthesis 2001 comma 41.5 right-parenthesis, left-parenthesis 2002 comma 43.5 right-parenthesis, left-parenthesis 2003 comma 43.5 right-parenthesis, and left-parenthesis 2004 comma 45.8 right-parenthesis.
B.
distance graph
The x-axis shows numbers from 1997 to 2004 with a step size of 1. It is labeled Year, The y-axis shows numbers from 39 to 46 with a step size of 1. It is labeled Distance (m), The points shown are approximately left-parenthesis 1997 comma 39.8 right-parenthesis, left-parenthesis 1998 comma 41.3 right-parenthesis, left-parenthesis 1999 comma 40.3 right-parenthesis, left-parenthesis 2000 comma 40.5 right-parenthesis, left-parenthesis 2001 comma 43.5 right-parenthesis, left-parenthesis 2002 comma 43.5 right-parenthesis, left-parenthesis 2003 comma 41.5 right-parenthesis, and left-parenthesis 2004 comma 45.8 right-parenthesis.
C.
distance graph
The x-axis shows numbers from 1997 to 2004 with a step size of 1. It is labeled Year, The y-axis shows numbers from 39 to 46 with a step size of 1. It is labeled Distance (m), The points shown are approximately left-parenthesis 1997 comma 41.8 right-parenthesis, left-parenthesis 1998 comma 41.8 right-parenthesis, left-parenthesis 1999 comma 40.3 right-parenthesis, left-parenthesis 2000 comma 40.5 right-parenthesis, left-parenthesis 2001 comma 41.5 right-parenthesis, left-parenthesis 2002 comma 43.5 right-parenthesis, left-parenthesis 2003 comma 43.5 right-parenthesis, and left-parenthesis 2004 comma 45.8 right-parenthesis.
D.
distance graph
B. A scatter plot is shown. The x-axis shows numbers from 1997 to 2004 with a step size of 1. It is labeled Year. The y-axis shows numbers from 39 to 46 with a step size of 1. It is labeled Distance (m). The points shown are approximately (1997, 39.75), (1998, 41.25), (1999, 40.25), (2000, 40.5), (2001, 43.5), (2002, 43.5), (2003, 41.5), and (2004, 45.75).
The table shows the relationship between the number of days a plant grows and its height. Graph the data in a scatter plot and describe the trend shown by the graph.
# of Days Plant Height (cm)
0 5
2 6
4 8
5 10
6 13
7 14
8 17
A. A scatter plot of the height of a plant over 8 days is shown. The x-axis is labeled # of Days and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Plant Height (cm) and has numbers from 0 to 20 with a step size of 5. The scatter plots shows these approximate points: left-parenthesis 0 comma 5 right-parenthesis, left-parenthesis 2 comma 6 right-parenthesis, left-parenthesis 4 comma 8 right-parenthesis, left-parenthesis 5 comma 10 right-parenthesis, left-parenthesis 6 comma 13 right-parenthesis, left-parenthesis 7 comma 14 right-parenthesis, and left-parenthesis 8 comma 17.5 right-parenthesis.
The scatter plot shows a negative trend. As the number of days increases, the height of the plant decreases.
B. A scatter plot of the height of a plant over 8 days is shown. The x-axis is labeled # of Days and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Plant Height (cm) and has numbers from 0 to 20 with a step size of 5. The scatter plots shows these approximate points: left-parenthesis 0 comma 5 right-parenthesis, left-parenthesis 2 comma 6 right-parenthesis, left-parenthesis 4 comma 8 right-parenthesis, left-parenthesis 5 comma 10 right-parenthesis, left-parenthesis 6 comma 13 right-parenthesis, left-parenthesis 7 comma 14 right-parenthesis, and left-parenthesis 8 comma 17.5 right-parenthesis.
The scatter plot shows a positive trend. As the number of days increases, the height of the plant increases.
C. A scatter plot of the height of a plant over 8 days is shown. The x-axis is labeled # of Days and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Plant Height (cm) and has numbers from 0 to 20 with a step size of 5. The scatter plots shows these approximate points: left-parenthesis 0 comma 5 right-parenthesis, left-parenthesis 2 comma 8 right-parenthesis, left-parenthesis 4 comma 11 right-parenthesis, left-parenthesis 5 comma 12.5 right-parenthesis, left-parenthesis 6 comma 14 right-parenthesis, left-parenthesis 7 comma 16 right-parenthesis, and left-parenthesis 8 comma 17 right-parenthesis.
The scatter plot shows a negative trend. As the number of days increases, the height of the plant decreases.
D. A scatter plot of the height of a plant over 8 days is shown. The x-axis is labeled # of Days and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Plant Height (cm) and has numbers from 0 to 20 with a step size of 5. The scatter plots shows these approximate points: left-parenthesis 0 comma 5 right-parenthesis, left-parenthesis 2 comma 8 right-parenthesis, left-parenthesis 4 comma 11 right-parenthesis, left-parenthesis 5 comma 12.5 right-parenthesis, left-parenthesis 6 comma 14 right-parenthesis, left-parenthesis 7 comma 16 right-parenthesis, and left-parenthesis 8 comma 17 right-parenthesis.
The scatter plot shows a positive trend. As the number of days increases, the height of the plant increases.
A. A scatter plot of the height of a plant over 8 days is shown. The x-axis is labeled # of Days and has numbers from 0 to 10 with a step size of 2. The y-axis is labeled Plant Height (cm) and has numbers from 0 to 20 with a step size of 5. The scatter plot shows these approximate points: (0, 5), (2, 6), (4, 8), (5, 10), (6, 13), (7, 14), and (8, 17.5).
The scatter plot shows a positive trend. As the number of days increases, the height of the plant increases.
To determine which histogram represents the given data, we need to analyze the frequency table.
The frequency table shows the number of miles driven to work each day and the corresponding frequency. It is divided into six categories: 0-5, 6-10, 11-15, 16-20, 21-25, and 26-30.
Now, let's compare the frequency values in the frequency table with the heights of the rectangles or bars in each histogram option.
Option A:
- The rectangle spanning the 0-5 partition has a height of 3.
- The rectangle spanning the 5-10 partition has a height of 8.
- The rectangle spanning the 10-15 partition has a height of 8.
- The rectangle spanning the 15-20 partition has a height of 8.
- The rectangle spanning the 20-25 partition has a height of 5.
- The rectangle spanning the 25-30 partition has a height of 1.
Option B:
- The rectangle spanning the 0-5 partition has a height of 2.
- The rectangle spanning the 5-10 partition has a height of 8.
- The rectangle spanning the 10-15 partition has a height of 8.
- The rectangle spanning the 15-20 partition has a height of 4.
- The rectangle spanning the 20-25 partition has a height of 5.
- The rectangle spanning the 25-30 partition has a height of 3.
Option C:
- The rectangle spanning the 5-10 partition has a height of 5.
- The rectangle spanning the 10-15 partition has a height of 8.
- The rectangle spanning the 15-20 partition has a height of 4.
- The rectangle spanning the 20-25 partition has a height of 5.
- The rectangle spanning the 25-30 partition has a height of 3.
Option D:
The histogram is not described in the question or frequency table, so it cannot be the correct answer.
Considering the frequency values in the frequency table, Option A is the correct histogram representation.