Anndrei101906idn
Answered

Makahanap ng mga solusyon sa iyong mga problema sa tulong ng mga eksperto ng IDNStudy.com. Magtanong ng anumang bagay at makatanggap ng kumpleto at eksaktong sagot mula sa aming komunidad ng mga propesyonal.

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