descriptive statistics\nconstructing a frequency distribution and a histogram\nnumber of miles\n10 6 19 11 9…
descriptive statistics\nconstructing a frequency distribution and a histogram\nnumber of miles\n10 6 19 11 9 8 7 6\n3 13 14 3 9 13 8 14\n(a) complete the grouped frequency distribution for the data. (note that the class width is 4.)\nnumber of miles frequency\n0.5 - 4.5 \n4.5 - 8.5 \n8.5 - 12.5 \n12.5 - 16.5 \n16.5 - 20.5 \n(b) construct a histogram for the data.\nfrequency\n6\n5\n4\n3\n2\n1\n0\n0.5 4.5 8.5 12.5 16.5 20.5\nnumber of miles
Answer
Explanation:
Step1: Count data in 0.5 - 4.5
The values in the range 0.5 - 4.5 are 3, 3. So the frequency is 2.
Step2: Count data in 4.5 - 8.5
The values in the range 4.5 - 8.5 are 6, 6, 7, 8, 8. So the frequency is 5.
Step3: Count data in 8.5 - 12.5
The values in the range 8.5 - 12.5 are 9, 9, 10, 11. So the frequency is 4.
Step4: Count data in 12.5 - 16.5
The values in the range 12.5 - 16.5 are 13, 13, 14, 14. So the frequency is 4.
Step5: Count data in 16.5 - 20.5
The value in the range 16.5 - 20.5 is 19. So the frequency is 1.
Answer:
| Number of miles | Frequency |
|---|---|
| 0.5 - 4.5 | 2 |
| 4.5 - 8.5 | 5 |
| 8.5 - 12.5 | 4 |
| 12.5 - 16.5 | 4 |
| 16.5 - 20.5 | 1 |
For part (b), to construct the histogram:
- Draw bars with bases on the intervals 0.5 - 4.5, 4.5 - 8.5, 8.5 - 12.5, 12.5 - 16.5, 16.5 - 20.5.
- The heights of the bars should be 2, 5, 4, 4, 1 respectively corresponding to the frequencies calculated above.