The employees of a manufacturing company pledged the following donations in peso for the establishment of a community pantry: 100, 400, 250, 50, 200, 300, 100, 50, 150, 250, 500, 100, 300, 50, and 150. Using the employees’ contributions, calculate and interpret the following: a.) upper quartile b.) 7th decile c.) 35th percentile Solution: 50, 50, 50, 100, 100, 100, 150, 150, 200, 250, 250, 300, 300, 400, 500 a. Upper quartile or ?3 ?? = ? 4 (? + 1) ?3 = 3 4 (15 + 1) = 3 4 (16) = 48 4 = 12 ?3 is in the 12th position. Therefore, ?3 = 300. b. 7 th decile or ?7 ?? = ? 10 (? + 1) ?7 = 7 10 (15 + 1) = 7 10 (16) = 112 10 = 11.2 Interpolate: 11.2nd position is between the 11th and 12th position which are 250 and 300, respectively. 300-250=50 then 250+0.2=250.2. Hence, D7=250.2 c. 35th percentile or ?35 ?? = ? 100 (? + 1) ?35 = 35 100 (15 + 1) = 7 20 (16) = 112 20 = 5.6 Interpolate: 5.6th position is between the 5th and 6th position which are 100 and 100, respectively. Hence, P35=100. Guide Questions: 1. How did you determine the value of the upper quartile, 7th decile and the 35th percentile? 2. How will you interpret the results?
The employees of a manufacturing company pledged the following donations in peso for the establishment of a community pantry: 100, 400, 250, 50, 200, 300, 100, 50, 150, 250, 500, 100, 300, 50, and 150. Using the employees’ contributions, calculate and interpret the following: a.) upper quartile b.) 7th decile c.) 35th percentile Solution: 50, 50, 50, 100, 100, 100, 150, 150, 200, 250, 250, 300, 300, 400, 500 a. Upper quartile or ?3 ?? = ? 4 (? + 1) ?3 = 3 4 (15 + 1) = 3 4 (16) = 48 4 = 12 ?3 is in the 12th position. Therefore, ?3 = 300. b. 7 th decile or ?7 ?? = ? 10 (? + 1) ?7 = 7 10 (15 + 1) = 7 10 (16) = 112 10 = 11.2 Interpolate: 11.2nd position is between the 11th and 12th position which are 250 and 300, respectively. 300-250=50 then 250+0.2=250.2. Hence, D7=250.2 c. 35th percentile or ?35 ?? = ? 100 (? + 1) ?35 = 35 100 (15 + 1) = 7 20 (16) = 112 20 = 5.6 Interpolate: 5.6th position is between the 5th and 6th position which are 100 and 100, respectively. Hence, P35=100. Guide Questions: 1. How did you determine the value of the upper quartile, 7th decile and the 35th percentile? 2. How will you interpret the results?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The employees of a manufacturing company pledged the following donations in peso
for the establishment of a community pantry: 100, 400, 250, 50, 200, 300, 100, 50, 150, 250,
500, 100, 300, 50, and 150. Using the employees’ contributions, calculate and interpret the
following:
a.) upper quartile b.) 7th decile c.) 35th percentile
Solution:
50, 50, 50, 100, 100, 100, 150, 150, 200, 250, 250, 300, 300, 400, 500
a. Upper quartile or ?3
?? =
?
4
(? + 1) ?3 =
3
4
(15 + 1) =
3
4
(16) =
48
4
= 12
?3 is in the 12th position. Therefore, ?3 = 300.
b. 7
th decile or ?7
?? =
?
10
(? + 1) ?7 =
7
10
(15 + 1) =
7
10
(16) =
112
10
= 11.2
Interpolate: 11.2nd position is between the 11th and 12th position which are 250 and
300, respectively. 300-250=50 then 250+0.2=250.2. Hence, D7=250.2
c. 35th percentile or ?35
?? =
?
100
(? + 1) ?35 =
35
100
(15 + 1) =
7
20
(16) =
112
20
= 5.6
Interpolate: 5.6th position is between the 5th and 6th position which are 100 and 100,
respectively. Hence, P35=100.
Guide Questions:
1. How did you determine the value of the upper quartile, 7th decile and the 35th
percentile?
2. How will you interpret the results?
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