Solved on Mar 13, 2024
Create a box plot with min and max as whiskers for the data: .
STEP 1
Assumptions
1. We are given a set of numbers: .
2. We need to create a box plot with the minimum and maximum values as the endpoints of the whiskers.
3. We will calculate the quartiles (Q1, median/Q2, Q3) to construct the box plot.
4. The box plot will include the median, the upper and lower quartiles, and the whiskers extending to the minimum and maximum values.
STEP 2
First, we need to order the numbers from smallest to largest to find the quartiles and the min and max values.
STEP 3
Identify the minimum and maximum values from the ordered list.
- Minimum (Min) value:
- Maximum (Max) value:
STEP 4
Calculate the median (Q2), which is the middle value of the ordered list. Since there are 11 numbers, the median will be the 6th number.
STEP 5
To find the lower quartile (Q1), we take the median of the first half of the data (not including the median if the number of data points is odd). The first half of the data is .
STEP 6
To find the upper quartile (Q3), we take the median of the second half of the data (not including the median if the number of data points is odd). The second half of the data is .
STEP 7
Now we have all the necessary components to create the box plot: - Minimum value (Min): - Lower quartile (Q1): - Median (Q2): - Upper quartile (Q3): - Maximum value (Max):
STEP 8
Draw a number line that is long enough to include the minimum and maximum values.
STEP 9
Mark the minimum value and the maximum value on the number line to represent the endpoints of the whiskers.
STEP 10
Draw a box from the lower quartile (Q1) to the upper quartile (Q3).
STEP 11
Draw a line inside the box at the median (Q2) value.
STEP 12
Extend whiskers from the ends of the box to the minimum and maximum values.
The box plot is now complete, with the box representing the interquartile range (IQR), the line inside the box representing the median, and the whiskers extending to the minimum and maximum values.
Was this helpful?
