Strength and Weakness of Measure of Dispersion (Essay Sample)
SECTION A
QUESTION A 1
A university has marks of 38%, 49%, 51%, 53%, and 60%in five of her six subjects
a) The mark student need in 6th subject to obtain an overall average of 50%
b) A module is assessed by an assignment-25% of the module’s marks, and an examination-75% of modules marks. Student awarded 22% for assignment. So, mark need to get overall mark of 40%.
The mark they need in examination to obtain 40% for module is 18%
c) Students mark are 38%, 49%, 51%,53%,55% and 60%, it is not possible to find the mode because in this data given there is no number existing frequently or more than one time. We know that mode in statistics is the number of occurrences of value in a data and so no value exists more than once.
QUESTION A2
Strength and weakness of measure of dispersion
i. Range
Means the change or difference of the value between the biggest and the smallest one in the data set.
The essential strength is that it is easily manipulated in calculation,
Weakness - Occupants get it sensitive to and hardly utilize entire values in a given data. Range gives more information to furnish the values of maximum and minimum values instead of furnish the range (Kohli, 2016).
ii. Interquartile range
Strength- It is utilized as a variability evaluation or measure provided the extremum values are not being entered precisely, for instance, in a situation of changeable class intervals in the distribution of frequency. Another strength is that it hardly gets influenced by extremum values (Gordon, 2015).
Weakness- It as an evaluation of dispersion is that it is hardly tractable to mathematical calculations.
iii. Standard deviation
Strength-It is a very important evaluation of dispersion because, when the value emanating from a distribution which is normalized, then around 70% of reflections is alongside mean of approximately plus or minus one (± 1) of it. 90% of reflections fall in within a mean in the range of plus or minus 2 (± 2) of it and reflections of 98% of its fall in between mean ± 3 of it. Another strength is that that together with mean, possibly it may be utilized to discover lopsidedness (Kohli, 2016).
Weakness-It is an incompatible or inappropriate measure of dispersion
for skewed data.
QUESTON A3
Correlation Errors
a) Existence of strong correlation of +0.95 between X and Y, profs that X causes. The correlation is measuring the amount of linear association between two variables.
This correlation is stronger because as the value K approaches positive one (+1), then linear relationship grows to be stronger. Error is that if X is causing Y then correlation might not exist (Berger, 2016).
b) Correlation between X and Y is +0.5 and correlation Y and X is -0.95.
Existence of strong correlation, which is value +0.95 between X and Y and we get record of 0 to -1. Which is -0.59 explain that the duo sureties move in directions of contradiction. If K is –0.95, the relation is noted to be absolutely correlated negatively.
Error- When there is an increase of the single variable, another variable reduces in value or diminishes with the similar magnitude, and contrariwise. all the same, the level to which duo sureties are correlated negatively may vary for a period of time and are nearly imprecisely correlated in the entire time.
c) Correlation between X and Y is 0.95m/s2
Existence of strong speed correlation of +0.95m/s2 between X and Y, profs that X causes the speed correlation is measuring the amount of linear speed association between two variables.
This correlation is stronger because as K approaching +1, we get stronger relationship of the linear speed. The error is that if X is causing Y then speed correlation might not exist.
Question A4
Cost increase in a company producing models of processors CP1 an CP Deluxe in ration of 65:35
Year
2014
2015
2016
2017
2018
2019
2010
Price (2014=100)
100.0
105.1
107.4
109.8
112.5
115.8
"?
a) We study the trend in the initial table given the n adopt a formula to Rebase the table of index number on 2009=100
Year
2019
2020
2021
2022
2023
2023
2024
Price (2019=100)
115.8
120.9
123.2
125.6
128.3
131.6
"?
b) CP1 Price percentage increases and calculated by adding three components prices, X, Y, and Z.
Component
2019 Price(euro)
2020 price (euro)
Weight
X
11.35
11.55
20
Y
8.15
8.35
65
Z
6.40
6.48
15
Total
37.45
26.38
100
Calculate a price index number for CP1 in 2020 based on 2019.
To prorate the Price Index, we the price of the year market cluster divided into price of year market cluster of interest and ensue by multiply it by 100. In this situation we get in the 2020 price or cost index and put blueprint to use 2019 as the foundation year (Church, 2016).
Price index number for CP1 in 2020 based on 2019 is 70
SECTION A
QUESTION A 1
A university has marks of 38%, 49%, 51%, 53%, and 60%in five of her six subjects
* The mark student need in 6th subject to obtain an overall average of 50%
38%+49%+51%+53%+60%+K6=50%
251+K6=50%
251+K=300%
K=300-251%=49%
The mark of sixth subject is 49%
* A module is assessed by an assignment-25% of the module’s marks, and an examination-75% of modules marks. Student awarded 22% for assignment. So, mark need to get overall mark of 40%.
22%+E=40%, E=40%-22%=18%
E=18%
The mark they need in examination to obtain 40% for module is 18%
* Students mark are 38%, 49%, 51%,53%,55% and 60%, it is not possible to find the mode because in this data given there is no number existing frequently or more than one time. We know that mode in statistics is the number of occurrences of value in a data and so no value exists more than once.
QUESTION A2
Strength and weakness of measure of dispersion
* Range
Means the change or difference of the value between the biggest and the smallest one in the data set.
The essential strength is that it is easily manipulated in calculation,
Weakness - Occupants get it sensitive to and hardly utilize entire values in a given data. Range gives more information to furnish the values of maximum and minimum values instead of furnish the range (Kohli, 2016).
* Interquartile range
Strength- It is utilized as a variability evaluation or measure provided the extremum values are not being entered precisely, for instance, in a situation of changeable class intervals in the distribution of frequency. Another strength is that it hardly gets influenced by extremum values (Gordon, 2015).
Weakness- It as an evaluation of dispersion is that it is hardly tractable to mathematical calculations.
* Standard deviation
Strength-It is a very important evaluation of dispersion because, when the value emanating from a distribution which is normalized, then around 70% of reflections is alongside mean of approximately plus or minus one (± 1) of it. 90% of reflections fall in within a mean in the range of plus or minus 2 (± 2) of it and reflections of 98% of its fall in between mean ± 3 of it. Another strength is that that together with mean, possibly it may be utilized to discover lopsidedness (Kohli, 2016).
Weakness-It is an incompatible or inappropriate measure of dispersion
for skewed data.
QUESTON A3
Correlation Errors
* Existence of strong correlation of +0.95 between X and Y, profs that X causes. The correlation is measuring the amount of linear association between two variables.
This correlation is stronger because as the value K approaches positive one (+1), then linear relationship grows to be stronger. Error is that if X is causing Y then correlation might not exist (Berger, 2016).
* Correlation between X and Y is +0.5 and correlation Y and X is -0.95.
Existence of strong correlation, which is value +0.95 between X and Y and we get record of 0 to -1. Which is -0.59 explain that the duo sureties move in directions of contradiction. If K is –0.95, the relation is noted to be absolutely correlated negatively.
Error- When there is an increase of the single variable, another variable reduces in value or diminishes with the similar magnitude, and contrariwise. all the same, the level to which duo sureties are correlated negatively may vary for a period of time and are nearly imprecisely correlated in the entire time.
* Correlation between X and Y is 0.95m/s2
Existence of strong speed correlation of +0.95m/s2 between X and Y, profs that X causes the speed correlation is measuring the amount of linear speed association between two variables.
This correlation is stronger because as K approaching +1, we get stronger relationship of the linear speed. The error is that if X is causing Y then speed correlation might not exist.
Question A4
Cost increase in a company producing models of processors CP1 an CP Deluxe in ration of 65:35
Year
2014
2015
2016
2017
2018
2019
2010
Price (2014=100)
100.0
105.1
107.4
109.8
112.5
115.8
"?
* We study the trend in the initial table given the n adopt a formula to Rebase the table of index number on 2009=100
Year
2019
2020
2021
2022
2023
2023
2024
Price (2019=100)
115.8
120.9
123.2
125.6
128.3
131.6
"?
* CP1 Price percentage increases and calculated by adding three components prices, X, Y, and Z.
Component
2019 Price(euro)
2020 price (euro)
Weight
X
11.35
11.55
20
Y
8.15
8.35
65
Z
6.40
6.48
15
Total
37.45
26.38
100
Calculate a price index number for CP1 in 2020 based on 2019.
To prorate the Price Index, we the price of the year market cluster divided into price of year market cluster of interest and ensue by multiply it by 100. In this situation we get in the 2020 price or cost index and put blueprint to use 2019 as the foundation year (Church, 2016).
Price Index for 2020=Market Baseket for 2020Market Basket for 2019×100=26.3837.45×100=70.44
Price Index for 2020=Market Baseket for 2020Market Basket for 2019×100
26.3837.45×100=70.44
Price index number for CP1 in 2020 based on 2019 is 70
* CP Deluxe has risen in price by 4.1% in 2020 compared to 2019.Produing an index number based on 2014=100 involve a percent increase to prices of 2020 and 2019
Component
2019 Price(euro)
2020 price (euro)
Weight
X
11.81535
12.02355
20
Y
8.48415
8.69235
65
Z
6.40
6.74568
15
Total
26.59568
27.46158
100
Price Index for 2020=Market Baseket for 2020Market Basket for 2019×100=27.4615837.4526.59568×100=70.44
27.4615826.59568×100=1.032557919180
Index number for CP1 when there is 4.1 increment
Index number is 1.
Question B1
Frequency distribution and cumulative frequency
Examination mark
Number of students
20<30
8
30<40
10
40<50
12
50<60
22
60<70
24
70<80
14
80<100
10
* Estimation of marks;
lower quartile marks- from the data set [8,10,10,12,14,22,24] the lower quartile is 10 marks
Median marks-The median 50 marks
Upper quartile marks-from the data set [8,10,10,12,14,22,24.14] marks is the upper quartile
* Calculate estimate of the mean mark
Examination mark
Mid Class (c)
Number of students(f)
CF
20<30
25
8
200
30<40
35
10
310
40<50
45
12
540
50<60
55
22
1210
60<70
65
24
1560
70<80
75
14
1050
80<100
85
10
850
100
5,720
Mean Mark=CFF
=5720100=57.2
Mean is 57.2 marks
* Examination marks bet...
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