Direct Answer!
Q₁ = 26.25
Q₁ = 26.25Q₂ = 38.75
Q₁ = 26.25Q₂ = 38.75Q = 70
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To compute for Q₁, Q₂, and Q
First, you need to calculate the total number of games won by the 40 Filipino boxers.
Total number of games won = (2 * 75) + (6 * 65) + (10 * 55) + (9 * 45) + (8 * 35) + (5 * 25)
Total number of games won = 150 + 390 + 550 + 405 + 280 + 125
Total number of games won = 1900
Now, to find Q₁ (25th percentile)
Find the position of 25% of the data.
Q₁ position = 0.25 * 40
Q₁ position = 10
This means that Q₁ falls within the 13th class interval (30-39) with 8 frequency.
To find Q₁, use the formula:
Q₁ = L + ((N/4 - F) / f) * w
Now, to calculate it:
Q₁ = 30 + ((10 - 13) / 8) * 10
Q₁ = 30 + (-0.375) * 10
Q₁ = 30 - 3.75
Q₁ = 26.25
To find Q₂ (50th percentile, or the median),
Find the position of 50% of the data:
Q₂ position = 0.5 * 40
Q₂ position = 20
This means that Q₂ also falls within the 13th class interval (30-39).
Using the same formula:
Q₂ = 30 + ((20 - 13) / 8) * 10
Q₂ = 30 + (0.875) * 10
Q₂ = 30 + 8.75
Q₂ = 38.75
To find Q (75th percentile)
Find the position of 75% of the data:
Q position = 0.75 * 40
Q position = 30
This means that Q falls within the 10th class interval (20-29) with 5 frequency.
Usig the formula:
Q = 20 + ((30 - 5) / 5) * 10
Q = 20 + (5) * 10
Q = 20 + 50
Q = 70
