To construct a frequency distribution with a class width of 10 and using 30.0 as the lower class limit for the first class, we first create the class intervals. Then we will count how many data points fall into each interval.
Class Intervals
- Class 1: 30.0 - 39.9
- Class 2: 40.0 - 49.9
- Class 3: 50.0 - 59.9
- Class 4: 60.0 - 69.9
- Class 5: 70.0 - 79.9
- Class 6: 80.0 - 89.9
- Class 7: 90.0 - 99.9
- Class 8: 100.0 - 109.9
- Class 9: 110.0 - 119.9
- Class 10: 140.0 - 149.9
Data Points
Now let's count how many data points fit into each class interval:
- 30.8
- 86.2
- 60.1
- 59.8
- 82.4
- 62.7
- 53.4
- 68.8
- 32.5
- 114.7
- 44.0
- 38.9
- 90.2
- 31.2
- 64.2
- 43.3
- 77.6
- 48.0
- 44.1
- 96.7
- 57.7
- 140.7
- 55.2
- 93.7
- 89.8
- 93.5
- 36.9
- 89.2
- 39.3
- 80.6
Counting Frequency
- 30.0 - 39.9: 6 (30.8, 32.5, 31.2, 38.9, 36.9, 39.3)
- 40.0 - 49.9: 5 (44.0, 44.1, 43.3, 48.0, 49.0)
- 50.0 - 59.9: 6 (53.4, 55.2, 57.7, 59.8, 60.1, 59.9)
- 60.0 - 69.9: 4 (62.7, 64.2, 68.8, 69.9)
- 70.0 - 79.9: 1 (77.6)
- 80.0 - 89.9: 6 (82.4, 86.2, 89.2, 89.8, 89.7, 80.6)
- 90.0 - 99.9: 5 (90.2, 96.7, 93.7, 93.5, 93.5)
- 100.0 - 109.9: 1 (114.7)
- 110.0 - 119.9: 0
- 140.0 - 149.9: 1 (140.7)
Frequency Distribution Table
Now we can summarize the results in a table format:
| Class | Frequency | |-----------------|----------| | 30.0 - 39.9 | 6 | | 40.0 - 49.9 | 5 | | 50.0 - 59.9 | 6 | | 60.0 - 69.9 | 4 | | 70.0 - 79.9 | 1 | | 80.0 - 89.9 | 6 | | 90.0 - 99.9 | 5 | | 100.0 - 109.9 | 1 | | 110.0 - 119.9 | 0 | | 140.0 - 149.9 | 1 |
This table provides a complete frequency distribution of the manufacturer's suggested retail prices for the BMW automobiles based on the specified class width and lower limit.