Math with Mr. J: Understanding Quartiles

What Are Quartiles?

• Quartiles divide data sets into four equal parts.
  • Lower Quartile (Q1): 25th percentile (1/4 mark)
  • Median (Q2): 50th percentile (middle of data)
  • Upper Quartile (Q3): 75th percentile (3/4 mark)

Importance of Quartiles

• Help in understanding and interpreting data.
• Serve as a foundation for more complex data topics.

Example 1: Odd Number of Data Points

• Begin by ordering the data set from least to greatest.
• Finding the Median (Q2):
  • For a data set with 9 numbers, the median is the 5th number.
  • Example: If the 5th number is 8, then 8 is the median.
• Finding the Lower Quartile (Q1):
  • Calculate the median of the lower half of the data set.
  • For an even number of numbers in the lower half, find the average of the two middle numbers.
  • Example: Median between 2 and 4 is 3.
• Finding the Upper Quartile (Q3):
  • Calculate the median of the upper half.
  • Example: Median between 10 and 14 is 12.
• Visualizing Quartiles:
  • Data is split into four equal parts between the 25th, 50th, and 75th percentiles.

Example 2: Even Number of Data Points

• Start by ordering the data set from least to greatest.
• Finding the Median (Q2):
  • For a data set with 8 numbers, find the average of the two middle numbers.
  • Example: Median between 21 and 28 is 24.5.
• Finding the Lower Quartile (Q1):
  • Calculate the median of the lower half.
  • Example: Median between 16 and 17 is 16.5.
• Finding the Upper Quartile (Q3):
  • Calculate the median of the upper half.
  • Example: Median between 31 and 39 is 35.
• Visualizing Quartiles:
  • Shows the division of data into four equal parts at the 25th, 50th, and 75th percentiles.

Conclusion

• Quartiles effectively divide a data set into four equal parts, making it easier to interpret and understand data distribution.
• Understanding how to calculate quartiles is foundational for statistical analysis and data interpretation.