2025 · Q97
Consider the grouped data: Distance classes 0-5, 5-10, 10-15, 15-20, 20-25, 25-30 with first group frequencies u, v, 11, 52, 75, 22 and second group 3u, 2v, 40, 50, 30, 28. Median of first group is 20.8 m, mean of second is 17.3 m. What is u?
Elementary MathematicsStatistics
- A1
- B2
- C3
- D4
Explanation
Median 20.8 lies in class 20-25: 20+[(N/2-cf)/75]*5=20.8 with N=u+v+160, cf=u+v+63 gives (u+v+160)/2-(u+v+63)=12, i.e. u+v=10. With the second group's mean 17.3, solving gives u=3 (v=7), which indeed yields median exactly 20.8. The median condition is the binding one.