Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
### Part a) Drawing the Cumulative Frequency Diagram
1. Create the Axes:
- Horizontal Axis (X-axis): Label it as "Distance (km)" and mark intervals from 0 to 20 km.
- Vertical Axis (Y-axis): Label it as "Cumulative Frequency" and mark intervals from 0 to 80.
2. Plot the Points on the Graph:
- Plot the point at (5 km, 6)
- Plot the point at (10 km, 30)
- Plot the point at (15 km, 60)
- Plot the point at (20 km, 80)
3. Join the Points with Straight Lines:
- Connect the points in sequence: (0,0) to (5,6), then (5,6) to (10,30), then (10,30) to (15,60), and finally (15,60) to (20,80).
### Part b) Estimating the Median and the Interquartile Range (IQR)
#### Finding the Median
1. Total Number of Observations:
- There are 80 total deliveries.
2. Median Position:
- The median is located at the 50th percentile, which is at the 0.5 80 = 40th observation.
3. Locate the 40th Observation on the Graph:
- Draw a horizontal line from the cumulative frequency value of 40 to intersect the cumulative frequency curve.
- Drop a vertical line from this intersection point down to the x-axis to read the corresponding distance.
- The distance corresponding to the 40th observation (from the graph) is approximately 11.67 km.
#### Finding Q1 and Q3
1. First Quartile (Q1) Position:
- Q1 is located at the 25th percentile, which is at the 0.25 80 = 20th observation.
2. Locate the 20th Observation on the Graph:
- Draw a horizontal line from the cumulative frequency value of 20 to intersect the cumulative frequency curve.
- Drop a vertical line from this intersection point down to the x-axis to read the corresponding distance.
- The distance corresponding to the 20th observation (from the graph) is approximately 5.75 km.
3. Third Quartile (Q3) Position:
- Q3 is located at the 75th percentile, which is at the 0.75 * 80 = 60th observation.
4. Locate the 60th Observation on the Graph:
- Draw a horizontal line from the cumulative frequency value of 60 to intersect the cumulative frequency curve.
- Drop a vertical line from this intersection point down to the x-axis to read the corresponding distance.
- The distance corresponding to the 60th observation (from the graph) is approximately 12.83 km.
5. Calculate the Interquartile Range (IQR):
- IQR = Q3 - Q1
- IQR ≈ 12.83 km - 5.75 km = 7.08 km
### Answers
- Median: 11.67 km
- IQR: 7.08 km
1. Create the Axes:
- Horizontal Axis (X-axis): Label it as "Distance (km)" and mark intervals from 0 to 20 km.
- Vertical Axis (Y-axis): Label it as "Cumulative Frequency" and mark intervals from 0 to 80.
2. Plot the Points on the Graph:
- Plot the point at (5 km, 6)
- Plot the point at (10 km, 30)
- Plot the point at (15 km, 60)
- Plot the point at (20 km, 80)
3. Join the Points with Straight Lines:
- Connect the points in sequence: (0,0) to (5,6), then (5,6) to (10,30), then (10,30) to (15,60), and finally (15,60) to (20,80).
### Part b) Estimating the Median and the Interquartile Range (IQR)
#### Finding the Median
1. Total Number of Observations:
- There are 80 total deliveries.
2. Median Position:
- The median is located at the 50th percentile, which is at the 0.5 80 = 40th observation.
3. Locate the 40th Observation on the Graph:
- Draw a horizontal line from the cumulative frequency value of 40 to intersect the cumulative frequency curve.
- Drop a vertical line from this intersection point down to the x-axis to read the corresponding distance.
- The distance corresponding to the 40th observation (from the graph) is approximately 11.67 km.
#### Finding Q1 and Q3
1. First Quartile (Q1) Position:
- Q1 is located at the 25th percentile, which is at the 0.25 80 = 20th observation.
2. Locate the 20th Observation on the Graph:
- Draw a horizontal line from the cumulative frequency value of 20 to intersect the cumulative frequency curve.
- Drop a vertical line from this intersection point down to the x-axis to read the corresponding distance.
- The distance corresponding to the 20th observation (from the graph) is approximately 5.75 km.
3. Third Quartile (Q3) Position:
- Q3 is located at the 75th percentile, which is at the 0.75 * 80 = 60th observation.
4. Locate the 60th Observation on the Graph:
- Draw a horizontal line from the cumulative frequency value of 60 to intersect the cumulative frequency curve.
- Drop a vertical line from this intersection point down to the x-axis to read the corresponding distance.
- The distance corresponding to the 60th observation (from the graph) is approximately 12.83 km.
5. Calculate the Interquartile Range (IQR):
- IQR = Q3 - Q1
- IQR ≈ 12.83 km - 5.75 km = 7.08 km
### Answers
- Median: 11.67 km
- IQR: 7.08 km
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
