In math, statistics especially, a five (5) number summary is five (5) numbers that show key points of quantitative data (must have at least five (5) numbers).
The five (5) numbers are as follows:
  • Minimum: Lowest value in the array of numbers.
  • Maximum: Highest value in the array of numbers.
  • Median: Middle value in the array of numbers.
  • First quartile (Q1): Value ranked between the minimum and median.
  • Third quartile (Q3): Value ranked between the maximum and median.
That is most likely not too helpful. I shall give an example!!!

A class is asked to find the five number summary of the students' heights. So... first we have to collect the data... this is the heights of students in my class (as found in centimeters)

188 176 173 175 175 179 183 176 192 164 183 173 172 184

so now we arrange this data in ascending order...

164 172 173 173 175 175 176 176 179 183 183 184 188 192

So, now we can find our five (5) numbers. The first number is the minimum, and that gives us 164 in this case. The last number is our maximum, and that is 192. Now, we have to find the median. That is the center number in the data. So, we have fourteen (14) heights, we'll divide that number by two (2) and count that many from the top and bottom (we will round down when we divide). The number between them will be out median. In this case, we get seven (7) from the top and bottom. Oh shit! That's between two numbers. The numbers are 176 and 176. To find what the median is we must take the average of the two (2) numbers. ( 176 + 176 ) / 2 = 176. Okay, so our median is 176! No to move on to our Q variables. We find these in much the same way as we did the median, but the median of the two (2) above said values instead. Doing this we find Q1 is 173 and Q3 is 183.

  • Minimum - 164
  • Q1 - 173
  • Median - 176
  • Q3 - 183
  • Maximum - 192


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