The monthly cost for health care for an employee and two dependents in a certain year is given in the following table.
Provider Cost Cost
Maxicare $415.20 Kaiser $433.66
cigna $ 424.91 Aetna 436.36
Health net $427.42 B/S $442.16
Pacific care $428.44 Omni 457.94
Redwood Plan $431.66 Lifguard 457.99
Draw a box plot for the monthly cost of helath care (ranked from Lowest to highest) Thank You
http://en.wikipedia.org/wiki/Box_plot
what do I need to do with the numbers above, do I add or subtract.
I know the lowest would be 415.20 the highest is 457.99
I think there is a Q1 Q2 and a Q3
To draw a box plot for the monthly cost of health care, we need to first rank the costs from lowest to highest. Let's arrange the costs in ascending order:
1. Maxicare: $415.20
2. Kaiser: $433.66
3. Cigna: $424.91
4. Aetna: $436.36
5. Health Net: $427.42
6. B/S: $442.16
7. Pacific Care: $428.44
8. Omni: $457.94
9. Redwood Plan: $431.66
10. Lifeguard: $457.99
Now we have the data values in ascending order. To construct a box plot, follow these steps:
Step 1: Calculate the median (middle value) of the data. In this case, since we have an even number of data points, we take the average of the two middle values. The middle values are Aetna ($436.36) and Health Net ($427.42), so the median is (436.36 + 427.42) / 2 = $431.89.
Step 2: Calculate the lower quartile (25th percentile) and upper quartile (75th percentile). To do this, divide the data into two halves. The lower half consists of Maxicare, Kaiser, Cigna, Aetna, and Health Net. The upper half consists of B/S, Pacific Care, Omni, Redwood Plan, and Lifeguard.
Lower Half:
Maxicare: $415.20
Kaiser: $433.66
Cigna: $424.91
Aetna: $436.36
Health Net: $427.42
Upper Half:
B/S: $442.16
Pacific Care: $428.44
Omni: $457.94
Redwood Plan: $431.66
Lifeguard: $457.99
To find the quartiles, we need to calculate the median of each half. The median of the lower half is (433.66 + 424.91) / 2 = $429.28. The median of the upper half is (431.66 + 442.16) / 2 = $436.91. Therefore, the lower quartile is $429.28 and the upper quartile is $436.91.
Step 3: Calculate the interquartile range (IQR). The IQR is the difference between the upper quartile and the lower quartile. In this case, IQR = $436.91 - $429.28 = $7.63.
Step 4: Determine the minimum value and the maximum value within the upper fence and lower fence. The upper fence is the upper quartile plus 1.5 times the IQR, and the lower fence is the lower quartile minus 1.5 times the IQR.
Upper Fence: $436.91 + (1.5 * $7.63) = $449.35
Lower Fence: $429.28 - (1.5 * $7.63) = $416.85
Step 5: Determine if there are any outliers. Data points outside the fences are considered outliers. In our case, there are no outliers.
Step 6: Draw the box plot. The box plot consists of a rectangle (the box) and vertical lines (whiskers) extending from the box. The rectangle represents the interquartile range (IQR), and the line within the rectangle represents the median.
- Draw a horizontal line and mark the minimum value ($415.20) and maximum value ($457.99).
- Draw a vertical line at the lower quartile ($429.28) and another vertical line at the upper quartile ($436.91).
- Connect these two vertical lines with a horizontal line to form the box.
- Draw a dot or a short horizontal line to represent the median ($431.89).
- Lastly, draw horizontal lines (whiskers) from the ends of the box to the minimum and maximum values.
This is how you can draw a box plot for the monthly cost of health care based on the given data.