Answer :
Certainly! Let's work through building a grouped frequency distribution and a histogram for the given data:
### Step-by-Step Solution:
#### (a) Complete the grouped frequency distribution for the data.
1. Data Set: We have the following temperatures:
105, 110, 97, 103, 112, 94, 94, 106, 105, 101, 96, 99, 104, 102, 99, 93.
2. Determine Class Intervals and Width:
- Given class width is 4.
- Use the midpoint of the classes to define ranges:
- (92.5, 96.5)
- (96.5, 100.5)
- (100.5, 104.5)
- (104.5, 108.5)
- (108.5, 112.5)
3. Calculate Frequency for Each Interval:
- Count how many temperatures fall into each interval.
- Interval (92.5, 96.5):
- Temperatures: 94, 94, 96, 93
- Frequency: 4
- Interval (96.5, 100.5):
- Temperatures: 97, 99, 99
- Frequency: 3
- Interval (100.5, 104.5):
- Temperatures: 101, 103, 104
- Frequency: 4
- Interval (104.5, 108.5):
- Temperatures: 105, 105, 106
- Frequency: 3
- Interval (108.5, 112.5):
- Temperatures: 110, 112
- Frequency: 2
4. Grouped Frequency Distribution Table:
- | Temperatures (in °F) | Frequency |
|----------------------|-----------|
| 92.5 - 96.5 | 4 |
| 96.5 - 100.5 | 3 |
| 100.5 - 104.5 | 4 |
| 104.5 - 108.5 | 3 |
| 108.5 - 112.5 | 2 |
#### (b) Construct a histogram for the data:
1. Create Histogram Representation:
- Make a bar for each interval on the x-axis.
- Height of each bar corresponds to the frequency of temperatures within that interval.
2. Visual Representation:
- Draw x-axis with intervals labeled: (92.5 - 96.5), (96.5 - 100.5), etc.
- Draw y-axis to represent frequency.
- Plot bars:
- (92.5 - 96.5): Bar with height of 4
- (96.5 - 100.5): Bar with height of 3
- (100.5 - 104.5): Bar with height of 4
- (104.5 - 108.5): Bar with height of 3
- (108.5 - 112.5): Bar with height of 2
By following these steps, you successfully complete the grouped frequency distribution and create a histogram for the temperature data.
### Step-by-Step Solution:
#### (a) Complete the grouped frequency distribution for the data.
1. Data Set: We have the following temperatures:
105, 110, 97, 103, 112, 94, 94, 106, 105, 101, 96, 99, 104, 102, 99, 93.
2. Determine Class Intervals and Width:
- Given class width is 4.
- Use the midpoint of the classes to define ranges:
- (92.5, 96.5)
- (96.5, 100.5)
- (100.5, 104.5)
- (104.5, 108.5)
- (108.5, 112.5)
3. Calculate Frequency for Each Interval:
- Count how many temperatures fall into each interval.
- Interval (92.5, 96.5):
- Temperatures: 94, 94, 96, 93
- Frequency: 4
- Interval (96.5, 100.5):
- Temperatures: 97, 99, 99
- Frequency: 3
- Interval (100.5, 104.5):
- Temperatures: 101, 103, 104
- Frequency: 4
- Interval (104.5, 108.5):
- Temperatures: 105, 105, 106
- Frequency: 3
- Interval (108.5, 112.5):
- Temperatures: 110, 112
- Frequency: 2
4. Grouped Frequency Distribution Table:
- | Temperatures (in °F) | Frequency |
|----------------------|-----------|
| 92.5 - 96.5 | 4 |
| 96.5 - 100.5 | 3 |
| 100.5 - 104.5 | 4 |
| 104.5 - 108.5 | 3 |
| 108.5 - 112.5 | 2 |
#### (b) Construct a histogram for the data:
1. Create Histogram Representation:
- Make a bar for each interval on the x-axis.
- Height of each bar corresponds to the frequency of temperatures within that interval.
2. Visual Representation:
- Draw x-axis with intervals labeled: (92.5 - 96.5), (96.5 - 100.5), etc.
- Draw y-axis to represent frequency.
- Plot bars:
- (92.5 - 96.5): Bar with height of 4
- (96.5 - 100.5): Bar with height of 3
- (100.5 - 104.5): Bar with height of 4
- (104.5 - 108.5): Bar with height of 3
- (108.5 - 112.5): Bar with height of 2
By following these steps, you successfully complete the grouped frequency distribution and create a histogram for the temperature data.