Statistics: Quartiles

Given the following set of data, find the median, upper and lower quartile, and the interquartile range.

Test Scores: 81, 78, 90, 96, 93, 98, 85, 100, 85, 92, ,89, 91, 92

Median: the middle data point when the data is in numerical order

Data in numerical order: 78, 81, 85, 85, 89, 90, 91, 92, 92, 93, 96, 98, 100

• • Thirteen data points, 7th point is median
  • Median=91 splits data into upper and lower halves
  • First Quartile: Median of the lower half, the lower half has 6 terms, The average of 3rd and 4th term is median =85
  • 2nd Quartile = Overall Median of data set =91
  • Third Quartile: Median of the upper half of 4th point of that group averaged is the 3rd quartile = =94.5
  • Interquartile range = Range between Q1 and Q2

Box and Whisker plot of Data