How to find a five-number summary in statistics: Overview
The five number summary consists of 5 items:
- The minimum.
- Q1 (the first quartile, or the 25% mark).
- The median.
- Q3 (the third quartile, or the 75% mark).
- The maximum.
The five number summary gives you a rough idea about what your data set looks like. for example, you’ll have your lowest value (the minimum) and the highest value (the maximum). Although it’s useful in itself, the main reason you’ll want to find a five-number summary is to find more useful statistics, like the interquartile range, sometimes called the middle fifty.
This how to article will guide you through how to find a five-number summary. Watch the video or read the steps below:
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:
- 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).
- 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.
Box and whisker chart
A box and whiskers chart is a visual representation of the summary.
When the Summary doesn’t exist
Sometimes, it’s impossible to find a five number summary. In order for the five numbers to exist, your data set must meet these two requirements:
- Your data must be univariate. In other words, the data must be a single variable. For example, this list of weights is one variable: 120, 100, 130, 145. IF you have a list of ages and you want to compare the ages to weights, it becomes bivariate. For example: age 1 (25 pounds), 5 (60 pounds), 15 (129 pounds). The matching pairs makes it impossible to find a five number summary.
- Your data must be ordinal, interval, or ratio.
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