Question

how to find the 5 numbers for your box plot.
step 1: put your numbers in ascending order (from smallest to largest). for this particular data - set, the order is: example 1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
step 2: find the minimum and maximum for your data set. now that your numbers are in order, this should be easy to spot.
in the example in step 1, the minimum (the smallest number) is 1 and the maximum (the largest number) is 27.
step 3: find the median. the median is the middle number by canceling numbers from each side. if you have two numbers left in the middle, find the mean. add the 2 numbers and divide by 2.
step 4: place parentheses around the numbers above and below the median (this is not necessary, but it makes q1 and q3 easier to find). (1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27).
step 5: find q1 and q3. q1 can be thought of as a median in the lower half of the data, and q3 can be thought of as a median for the upper half of data. (1, 2, 5, 6, 7), 9, (12,15,18,19,27).
step 6: write down your summary found in the above steps. minimum = 1, q1 = 5, median = 9, q3 = 18, and maximum = 27.
practice problems: create a box plot for the following problems

1. the data set represents the shoe sizes of 16 students in a fifth - grade physical education class.

4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8,
create a box plot to represent the distribution of the data.

Explanation:

Answer:

1. First, put the data in ascending - order: 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8.

• Minimum: 4
• Median: Since \(n = 16\) (even), median\(=\frac{7 + 7}{2}=7\)
• Lower - half data: 4, 5, 5, 5, 6, 6, 6, 7. Q1\(=\frac{5+6}{2}=5.5\)
• Upper - half data: 7, 7, 7, 7, 8, 8, 8. Q3\(=\frac{7 + 7}{2}=7\)
• Maximum: 8

Discipline: Mathematics, Sub - field: Statistics