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Five-number summary (video)
- Definition from Wikipedia
Five-number Summary
Step 1) Put the data in order from least to greatest value.
The five-number summary illustrates the variation, or the spread, or the range of a group of data. It contains the following information about a group of measurements or observations: minimum, first quartile, median, third quartile and the maximum. These five data points are used to draw a boxplot.
Example: Find the five-number summary from the following data: 75,82, 62, 55, 95, 99, 76, 82 and 81.
Example: Find the five-number summary from the following data: 75,82, 62, 55, 95, 99, 76, 82 and 81.
Step 1) Put the data in order from least to greatest value.
55, 62, 75, 76, 81, 82, 82, 95, 99
Step 2) The min and the max are easy... they are the first and last numbers respectively in your new ordered list. Minimum = 55 and the maximum = 99.
Step 3) The median of the data is that measurement which has half of the other measurements above it and half of the measurements below it. (Note** If there is an odd number of measurements there will be only one measurment that is the median, but if there is an even number of measurements then there will be two measurements that separate the data into two equal parts. When there are two median measurements, add them together and divide by two to get the single median measurement value.) Median = 81
Step 4) The first quartile (q1) is the measurement in the set of data that has 1/4th of the other measurements below it. A good short cut is to divide the number of terms
by four and always round up to the nearest whole number. n = 9 (9 measurements in this example)... So 9/4 = 2.25... rounds up to 3... so our third term is the first quartile.... q1 = 75
Step 5) The third quartile (q3) is the measurement in the set of data that has 3/4ths of other measurements below it (and 1/4th of the data above it.) A good shortcut is to divide the number of terms by four, multiply that quotient by three and always round up to the nearest whole number. n = 9 (9 measurements in this example)... So 9/4 = 2.25... times 3 = 6.75 which rounds up to 7... so our seventh term is the third quartile... q3 = 82
by four and always round up to the nearest whole number. n = 9 (9 measurements in this example)... So 9/4 = 2.25... rounds up to 3... so our third term is the first quartile.... q1 = 75
Step 5) The third quartile (q3) is the measurement in the set of data that has 3/4ths of other measurements below it (and 1/4th of the data above it.) A good shortcut is to divide the number of terms by four, multiply that quotient by three and always round up to the nearest whole number. n = 9 (9 measurements in this example)... So 9/4 = 2.25... times 3 = 6.75 which rounds up to 7... so our seventh term is the third quartile... q3 = 82
Step 6) Write the terms out like this: (min, q1, med,q3, max) (55, 75, 81, 82, 99).
Step 7) Draw the boxplot from the data in the five-number summary.
All done!
Video Example (English)
Video Example (Spanish)
Step 7) Draw the boxplot from the data in the five-number summary.
All done!
Video Example (English)
Video Example (Spanish)
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