Anndrei101906idn
Answered

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B. Compute for Q₁, Q₂ and Q, of the number of games won by 40 Filipino boxers.
Class no. of Wins
Frequency
cf
70-79
2
40
60-69
6
38
50-59
10
32
40-49
9
22
30-39
8
13
20-29
5
5

Sagot :

PatchouliKnowledgeidn

Direct Answer!

Q₁ = 26.25

Q₁ = 26.25Q₂ = 38.75

Q₁ = 26.25Q₂ = 38.75Q = 70

==========

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