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Question

Question: #LP: Find median ...

#LP: Find median

Answer

Median = 40+4013≈43.0840 + \frac{40}{13} \approx 43.08

Explanation

Solution

Solution Explanation

  1. Total Frequency:
      N=8+10+13+6+3=40N = 8 + 10 + 13 + 6 + 3 = 40.
      N/2=20N/2 = 20.

  2. Cumulative Frequency Table:
      0–20: 8
      20–40: 8+10=188+10 = 18
      40–60: 18+13=3118+13 = 31
      60–80: 31+6=3731+6 = 37
      80–100: 37+3=4037+3 = 40

  3. Median Class:
      The median falls in the 40–60 interval (since 31 ≥ 20).

  4. Parameters for the Formula:
      Lower limit, L=40L = 40
      Class width, h=60−40=20h = 60 - 40 = 20
      Frequency of median class, f=13f = 13
      Cumulative frequency before median class, cf=18cf = 18

  5. Median Formula:
      $$ \text{Median} = L + h \times \frac{(N/2 - cf)}{f}

6. **Substitute and Calculate:**   $$ \text{Median} = 40 + 20 \times \frac{(20 - 18)}{13} = 40 + 20 \times \frac{2}{13} = 40 + \frac{40}{13} \approx 43.08

Answer:
Median = 40+4013≈43.0840 + \frac{40}{13} \approx 43.08