Math Problem Statement

From a data set like this what is the Median (Q2), first quartile (Q1) and third Quartile(Q3):

  1. 1
  2. 9
  3. 10
  4. 12
  5. 13
  6. 14
  7. 20
  8. 21
  9. 26
  10. 27
  11. 28
  12. 30
  13. 32
  14. 35
  15. 36
  16. 36
  17. 37
  18. 40
  19. 40
  20. 42
  21. 42
  22. 45
  23. 47
  24. 48
  25. 50
  26. 51
  27. 52
  28. 52
  29. 53
  30. 57

Solution

For the given data set, the values are as follows:

  • First Quartile (Q1): 22.25
  • Median (Q2): 36.0
  • Third Quartile (Q3): 46.5

Would you like more details or have any questions? Here are some related questions to explore further:

  1. How do you calculate quartiles manually from a data set?
  2. What is the significance of the interquartile range (IQR) in statistics?
  3. How can quartiles help in detecting outliers?
  4. What is the difference between quartiles and percentiles?
  5. How does changing the dataset affect the quartile values?

Tip: Quartiles are used to understand the spread and distribution of data. The Interquartile Range (IQR) is particularly helpful in identifying outliers.

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Math Problem Analysis

Mathematical Concepts

Statistics
Quartiles
Data Distribution

Formulas

Q1 = (n+1) * 1/4
Q2 = Median
Q3 = (n+1) * 3/4

Theorems

Quartile Calculation Theorem

Suitable Grade Level

Grades 9-12

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