To create the box-and-whiskers plot, we need to find five specific numbers from the data set: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum.
Step 1: Order the data
First, let's list the numbers in order from least to greatest. Looking at the image, they are already sorted:
1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 8, 10
There are
14 numbers in total.
Step 2: Find the Median
The median is the middle number. Since there is an even number of data points (14), the median will be the average of the two middle numbers.
The two middle numbers are the 7th and 8th numbers.
- 7th number: 4
- 8th number: 5
Median = $(4 + 5) / 2 = 4.5$
Step 3: Find the Quartiles (Q1 and Q3)
The problem states to
exclude the median when computing the quartiles. This means we split the data into a lower half and an upper half, leaving out the middle values we just used.
*
Lower Half: 1, 2, 2, 2, 3, 3, 4 (7 numbers)
*
Upper Half: 5, 5, 6, 7, 8, 8, 10 (7 numbers)
Find Q1 (First Quartile):
Q1 is the median of the lower half. Since there are 7 numbers, the median is the exact middle one (the 4th number).
Lower Half: 1, 2, 2,
2, 3, 3, 4
Q1 = 2
Find Q3 (Third Quartile):
Q3 is the median of the upper half. Again, with 7 numbers, it is the exact middle one (the 4th number in this group).
Upper Half: 5, 5, 6,
7, 8, 8, 10
Q3 = 7
Step 4: Identify Minimum and Maximum
*
Minimum: The smallest number is
1.
*
Maximum: The largest number is
10.
Summary of Values for the Plot:
* Minimum (left whisker end):
1
* Q1 (left side of the box):
2
* Median (line inside the box):
4.5
* Q3 (right side of the box):
7
* Maximum (right whisker end):
10
Final Answer:
The box-and-whiskers plot should be drawn with the following positions:
- Left whisker dot at
1
- Left edge of the box at
2
- Vertical line inside the box at
4.5
- Right edge of the box at
7
- Right whisker dot at
10
Parent Tip: Review the logic above to help your child master the concept of create box and whisker plot.
