Math Lecture: Understanding Interquartile Range (IQR)

Overview

• Interquartile Range (IQR) measures the spread of the middle 50% of a data set.
• Range measures the spread of the entire data set.
• This lecture provides step-by-step examples with odd and even numbered data sets.

Example 1: Odd Numbered Data Set

1. Arranging Data

   • Ensure data is in ascending order (from least to greatest).
   • Example data set is already ordered.

2. Finding the Median

   • Median is the middle number of the data set.
   • For 7 numbers: 3 numbers on each side of the median.
   • Median (Q2) is 38 (50th percentile).

3. Finding Quartiles

   • Lower Quartile (Q1): Middle number of the lower half.
     • Q1 = 32.
   • Upper Quartile (Q3): Middle number of the upper half.
     • Q3 = 50.

4. Calculating the IQR

   • IQR = Q3 - Q1 = 50 - 32 = 18.
   • Visualize by dividing data into four equal parts.
   • IQR represents the range of the middle 50% of data.

Example 2: Even Numbered Data Set

1. Arranging Data

   • Verify data is ordered.

2. Finding the Median

   • For 10 numbers: Break in half, 5 numbers on each side.
   • Median is between two middle numbers (8 and 11).
   • Calculate median: (8 + 11) / 2 = 9.5.

3. Finding Quartiles

   • Lower Quartile (Q1): Median of lower 5 numbers.
     • Q1 = 6.
   • Upper Quartile (Q3): Median of upper 5 numbers.
     • Q3 = 14.

4. Calculating the IQR

   • IQR = Q3 - Q1 = 14 - 6 = 8.
   • Visual representation helps understand quartiles and IQR.

Conclusion

• IQR helps understand the spread of the central 50% of the data.
• Further resources available in linked videos for additional help with quartiles.
• Thanks for tuning in!