Question
Matt works at the Bounty Grove farm stand. He weighed a sample of 15 butternut squash and a sample of 15 acorn squash sold at the farm stand and recorded his results in these line plots.
Butternut
0:0
0.5:1
1:3
1.5:4
2:4
2.5:3
3:0
3.5:0
4:0
4.5:0
5:0
Weight (lbs.)
Acorn
0:0
0.5:0
1:0
1.5:0
2:4
2.5:3
3:1
3.5:2
4:3
4.5:2
5:0
Weight (lbs.)
Complete the table. Write your answers as whole numbers or decimals rounded to the nearest tenth.
Median Interquartile range
Butternut
Acorn 3 2
Butternut
0:0
0.5:1
1:3
1.5:4
2:4
2.5:3
3:0
3.5:0
4:0
4.5:0
5:0
Weight (lbs.)
Acorn
0:0
0.5:0
1:0
1.5:0
2:4
2.5:3
3:1
3.5:2
4:3
4.5:2
5:0
Weight (lbs.)
Complete the table. Write your answers as whole numbers or decimals rounded to the nearest tenth.
Median Interquartile range
Butternut
Acorn 3 2
Answers
GPT-4o mini
To find the median and interquartile range (IQR) for both the butternut squash and acorn squash, we need to analyze the data provided from the line plots.
### Butternut Squash Weights:
- 0 lbs: 0
- 0.5 lbs: 1
- 1 lb: 3
- 1.5 lbs: 4
- 2 lbs: 4
- 2.5 lbs: 3
- 3 lbs: 0
- 3.5 lbs: 0
- 4 lbs: 0
- 4.5 lbs: 0
- 5 lbs: 0
**Data Points for Butternut Squash (weights in lbs):**
- 1 (3 times)
- 1.5 (4 times)
- 2 (4 times)
- 2.5 (3 times)
This gives us the following list of weights:
- 1, 1, 1, 1.5, 1.5, 1.5, 1.5, 2, 2, 2, 2, 2.5, 2.5, 2.5
**Step 1: Find the Median**
To find the median:
- The median is the middle number. For 15 values, the median is the 8th value.
- In our sorted data: 1, 1, 1, 1.5, 1.5, 1.5, 1.5, **2**, 2, 2, 2, 2.5, 2.5, 2.5
Median = 2 lbs
**Step 2: Find the IQR**
To find the IQR:
- The first quartile (Q1) is the median of the first half of the data:
- Lower half: 1, 1, 1, 1.5, 1.5, 1.5, 1.5 (7 values)
- Median of lower half (4th value) = 1.5
- The third quartile (Q3) is the median of the second half of the data:
- Upper half: 2, 2, 2, 2, 2.5, 2.5, 2.5 (7 values)
- Median of upper half (4th value) = 2
- Calculate IQR:
IQR = Q3 - Q1 = 2 - 1.5 = 0.5
### Acorn Squash Weights:
- 0 lbs: 0
- 0.5 lbs: 0
- 1 lb: 0
- 1.5 lbs: 0
- 2 lbs: 4
- 2.5 lbs: 3
- 3 lbs: 1
- 3.5 lbs: 2
- 4 lbs: 3
- 4.5 lbs: 2
- 5 lbs: 0
**Data Points for Acorn Squash (weights in lbs):**
- 2 (4 times)
- 2.5 (3 times)
- 3 (1 time)
- 3.5 (2 times)
- 4 (3 times)
This gives us the following list of weights:
- 2, 2, 2, 2, 2.5, 2.5, 2.5, 3, 3.5, 4, 4, 4
**Step 1: Find the Median**
To find the median:
- In our sorted data: 2, 2, 2, 2, 2.5, 2.5, 2.5, **3**, 3.5, 4, 4, 4
Median = 3 lbs
**Step 2: Find the IQR**
To find the IQR:
- The first quartile (Q1) is the median of the first half of the data:
- Lower half: 2, 2, 2, 2, 2.5, 2.5 (6 values)
- Median of lower half (average of 3rd and 4th value) = (2 + 2) / 2 = 2
- The third quartile (Q3) is the median of the second half of the data:
- Upper half: 2.5, 3, 3.5, 4, 4, 4 (6 values)
- Median of upper half (average of 3rd and 4th value) = (3.5 + 4) / 2 = 3.75
- Calculate IQR:
IQR = Q3 - Q1 = 3.75 - 2 = 1.75
### Summary Table:
| | Median | Interquartile Range |
|----------|--------|---------------------|
| Butternut| 2 | 0.5 |
| Acorn | 3 | 1.75 |
Thus, the completed table will look like:
**Butternut**
- Median: 2
- Interquartile range: 0.5
**Acorn**
- Median: 3
- Interquartile range: 1.75
### Butternut Squash Weights:
- 0 lbs: 0
- 0.5 lbs: 1
- 1 lb: 3
- 1.5 lbs: 4
- 2 lbs: 4
- 2.5 lbs: 3
- 3 lbs: 0
- 3.5 lbs: 0
- 4 lbs: 0
- 4.5 lbs: 0
- 5 lbs: 0
**Data Points for Butternut Squash (weights in lbs):**
- 1 (3 times)
- 1.5 (4 times)
- 2 (4 times)
- 2.5 (3 times)
This gives us the following list of weights:
- 1, 1, 1, 1.5, 1.5, 1.5, 1.5, 2, 2, 2, 2, 2.5, 2.5, 2.5
**Step 1: Find the Median**
To find the median:
- The median is the middle number. For 15 values, the median is the 8th value.
- In our sorted data: 1, 1, 1, 1.5, 1.5, 1.5, 1.5, **2**, 2, 2, 2, 2.5, 2.5, 2.5
Median = 2 lbs
**Step 2: Find the IQR**
To find the IQR:
- The first quartile (Q1) is the median of the first half of the data:
- Lower half: 1, 1, 1, 1.5, 1.5, 1.5, 1.5 (7 values)
- Median of lower half (4th value) = 1.5
- The third quartile (Q3) is the median of the second half of the data:
- Upper half: 2, 2, 2, 2, 2.5, 2.5, 2.5 (7 values)
- Median of upper half (4th value) = 2
- Calculate IQR:
IQR = Q3 - Q1 = 2 - 1.5 = 0.5
### Acorn Squash Weights:
- 0 lbs: 0
- 0.5 lbs: 0
- 1 lb: 0
- 1.5 lbs: 0
- 2 lbs: 4
- 2.5 lbs: 3
- 3 lbs: 1
- 3.5 lbs: 2
- 4 lbs: 3
- 4.5 lbs: 2
- 5 lbs: 0
**Data Points for Acorn Squash (weights in lbs):**
- 2 (4 times)
- 2.5 (3 times)
- 3 (1 time)
- 3.5 (2 times)
- 4 (3 times)
This gives us the following list of weights:
- 2, 2, 2, 2, 2.5, 2.5, 2.5, 3, 3.5, 4, 4, 4
**Step 1: Find the Median**
To find the median:
- In our sorted data: 2, 2, 2, 2, 2.5, 2.5, 2.5, **3**, 3.5, 4, 4, 4
Median = 3 lbs
**Step 2: Find the IQR**
To find the IQR:
- The first quartile (Q1) is the median of the first half of the data:
- Lower half: 2, 2, 2, 2, 2.5, 2.5 (6 values)
- Median of lower half (average of 3rd and 4th value) = (2 + 2) / 2 = 2
- The third quartile (Q3) is the median of the second half of the data:
- Upper half: 2.5, 3, 3.5, 4, 4, 4 (6 values)
- Median of upper half (average of 3rd and 4th value) = (3.5 + 4) / 2 = 3.75
- Calculate IQR:
IQR = Q3 - Q1 = 3.75 - 2 = 1.75
### Summary Table:
| | Median | Interquartile Range |
|----------|--------|---------------------|
| Butternut| 2 | 0.5 |
| Acorn | 3 | 1.75 |
Thus, the completed table will look like:
**Butternut**
- Median: 2
- Interquartile range: 0.5
**Acorn**
- Median: 3
- Interquartile range: 1.75