Question

How to Find a Five-Number Summary: Steps

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. If you aren't sure how to find the median, see: How to find the mean mode and median.
Step 4: Place parentheses around the numbers above and below the median.(This is not technically 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.

Answer 1

To determine the five-number summary, organize the data in ascending order, then identify the minimum and maximum, calculate the median, and find the first and third quartiles which are the medians of the lower and upper halves of the dataset respectively.

Step-by-step explanation:

Steps to Find the Five-Number Summary

The five-number summary is a descriptive statistic that provides information about a dataset. It includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. These values help in understanding the distribution of data within a set and are used to create a box plot. To find the five-number summary, one must follow the steps below:

Organize the data in ascending order.

Identify the minimum (min) and maximum (max) values.

Determine the median (the middle value of the dataset).

Calculate the first quartile (Q1), which is the median of the lower half of the dataset.

Calculate the third quartile (Q3), which is the median of the upper half of the dataset.

Once these steps are completed, you can construct a box plot with these statistics, offering a visual representation of the dataset's distribution.

Example of Calculating Quartiles

Consider the following data set: 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5. The median is 7. By dividing this dataset into lower and upper halves, the first quartile (Q1) is 2, and the third quartile (Q3) is 9. Understanding these concepts allows us to comprehensively summarize and interpret the data.