Question No: Engro group, who recently sold its Engro foods start-up for a multi-million-rupees sum, is looking for another investment for fresh capital. It is considering an investment in coal (X) and solar (Y) power plant. For that they had a collected data on 5 different characteristics. Amanda has applied k-means clustering to this data for k = 2. Given the following data: Table 5.1ObservationsXY12018282033626422125144d) Visually represent the clusters of both parts (b) and (c).Note: I have already attach "B" and "c" part with images that have been solve. Only do "D" part for solve. b)Let the Initial two clusters be (1, 2) and (3,4, 5)The centrolds for two clusters are calculated as shown belowFor Cluster (1,2)X = = 14Y == 19For Cluster (3,4,5)X = J6+2tl4 = 243The centrold for two clusters are (14,19) for Cluster-1 (1,2) and (24,14) for Cluster-2 (3,4,5).c)The distance of observation from both cluster centrold Is calculated belowObservation (X, Y)Centroid – ICentroid – 2V(20 - 24) + (18 – 14)2 = 5. 66V(8 - 24) + (20 – 14) = 17.09(20, 18)V(20 – 14)2 + (18 - 19)? = 6. 08(8, 20)V(8 – 14) + (20 – 19) = 6. 08(36, 26)(36 14)2 + (26 - 19)2 = 23.08(36-24) +(26- 14) = 16. 97(22, 12) V(22 - 14) + (12 – 19) = 10. 63 V(22- 24 + (12 – 14) = 2. 83V(14 – 24 + (4 – 14) = 14. 1445(14, 4)V(14 – 14) + (4 – 19) = 15Here the distance of observation 1,3,4,5 are close to Cluster-2 (3,4,5). So the clusters are newlyformed as shown belowCluster-1 = {2)Cluster-2= {1,3,4, 5}The centrolds for two clusters are calculated as shown belowFor Cluster (2)X = 8Y = 20For Cluster (1,3,4,5)X = 0.36+22+ 14= 234Y =4 The centrold for two clusters are (8,20) for Cluster-1 (2) and (23,15) for Cluster-2 (1,3,4,5).The distance of observation from both cluster centrold Is calculated belowObservation (X, Y)Centroid – 1Centroid – 2I(20, 18) V(20 - 8) + (18 – 20) = 12. 16 V(20-23)2 + (18 – 15) = 4. 24(8, 20)V(8 - 8) + (20 – 20 = 0V(8 – 23)2 + (20 – 15) = 15. 81(36, 26)(36 – 8)* + (26 – 20) = 28. 64 V(36 – 23) + (26 – 15) = 17.03(22, 12) V(22 – 8)* + (12 – 20) = 16. 12 V(22 – 23)2 +(12 – 15)2 = 3. 16V14 – 8)* + (4 – 20) = 17.09 V(14 – 23) + (4 – 15) = 14.21V(14-23)+(4-15) - 14.215(14, 4)Here the distance of observation 1,3,4,5 are close to Cluster-2 (3,4,5). Thus the final clusters areCluster-1 = {2)Cluster-2 = {1,3,4,5}3.

Name: Question No: Engro group, who recently sold its Engro foods start-up f
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: Question No: Engro group, who recently sold its Engro foods start-up for a multi-million-rupees sum, is looking for another investment for fresh capital. It is considering an investment in coal (X) and solar (Y) power plant. For that they had a colle

K-mean clustering: K-mean clustering is an exploratory data analysis technique, it is done by…

Answered: Engro group, who recently sold its…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Topic Video

Question

Question No: Engro group, who recently sold its Engro foods start-up for a multi-million-rupees sum, is looking for another investment for fresh capital. It is considering an investment in coal (X) and solar (Y) power plant. For that they had a collected data on 5 different characteristics. Amanda has applied k-means clustering to this data for k = 2. Given the following data:
Table 5.1

Observations	X	Y
1	20	18
2	8	20
3	36	26
4	22	12
5	14	4

d) Visually represent the clusters of both parts (b) and (c).

Note: I have already attach "B" and "c" part with images that have been solve. Only do "D" part for solve.

b)
Let the Initial two clusters be (1, 2) and (3,4, 5)
The centrolds for two clusters are calculated as shown below
For Cluster (1,2)
X = = 14
Y =
= 19
For Cluster (3,4,5)
X = J6+2tl4 = 24
3
The centrold for two clusters are (14,19) for Cluster-1 (1,2) and (24,14) for Cluster-2 (3,4,5).
c)
The distance of observation from both cluster centrold Is calculated below
Observation (X, Y)
Centroid – I
Centroid – 2
V(20 - 24) + (18 – 14)2 = 5. 66
V(8 - 24) + (20 – 14) = 17.09
(20, 18)
V(20 – 14)2 + (18 - 19)? = 6. 08
(8, 20)
V(8 – 14) + (20 – 19) = 6. 08
(36, 26)
(36 14)2 + (26 - 19)2 = 23.08
(36-24) +(26- 14) = 16. 97
(22, 12) V(22 - 14) + (12 – 19) = 10. 63 V(22- 24 + (12 – 14) = 2. 83
V(14 – 24 + (4 – 14) = 14. 14
4
5
(14, 4)
V(14 – 14) + (4 – 19) = 15
Here the distance of observation 1,3,4,5 are close to Cluster-2 (3,4,5). So the clusters are newly
formed as shown below
Cluster-1 = {2)
Cluster-2= {1,3,4, 5}
The centrolds for two clusters are calculated as shown below
For Cluster (2)
X = 8
Y = 20
For Cluster (1,3,4,5)
X = 0.36+22+ 14
= 23
4
Y =
4

The centrold for two clusters are (8,20) for Cluster-1 (2) and (23,15) for Cluster-2 (1,3,4,5).
The distance of observation from both cluster centrold Is calculated below
Observation (X, Y)
Centroid – 1
Centroid – 2
I
(20, 18) V(20 - 8) + (18 – 20) = 12. 16 V(20-23)2 + (18 – 15) = 4. 24
(8, 20)
V(8 - 8) + (20 – 20 = 0
V(8 – 23)2 + (20 – 15) = 15. 81
(36, 26)
(36 – 8)* + (26 – 20) = 28. 64 V(36 – 23) + (26 – 15) = 17.03
(22, 12) V(22 – 8)* + (12 – 20) = 16. 12 V(22 – 23)2 +(12 – 15)2 = 3. 16
V14 – 8)* + (4 – 20) = 17.09 V(14 – 23) + (4 – 15) = 14.21
V(14-23)+(4-15) - 14.21
5
(14, 4)
Here the distance of observation 1,3,4,5 are close to Cluster-2 (3,4,5). Thus the final clusters are
Cluster-1 = {2)
Cluster-2 = {1,3,4,5}
3.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Means$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.