I have computed the statistics of both groups of students in a class, in which they are male and female students. How do you sort the data within each group to determine what proportion in each group is within one standard deviation of that group, and what is the sorted data look like base on the statistics? Are the proportions similar?
I have computed the statistics of both groups of students in a class, in which they are male and female students. How do you sort the data within each group to determine what proportion in each group is within one standard deviation of that group, and what is the sorted data look like base on the statistics? Are the proportions similar?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
I have computed the statistics of both groups of students in a class, in which they are male and female students.
How do you sort the data within each group to determine what proportion in each group is within one standard deviation of that group, and what is the sorted data look like base on the statistics? Are the proportions similar?

Transcribed Image Text:a. For male students
Interquartile range
IQR = Qs – QI
Mean
= 1.58 – 1.36 = 0.22
20.4
1.457143
N
14
GWA (x)
d
d?
(Deviation from the
mean)
-0.39714286
Median
Med =
1.42+1.45
1.435
1.06
1.1236
0.157722
1.33
1.7689
-0.12714286
0.016165
Minimum and maximum values
1.34
1.36
1.7956
-0.11714286
0.013722
Min (x) = 1.06
Маx (х) — 1.75
1.8496
-0.09714286
0.009437
1.38
1.9044
-0.07714286
0.005951
1.42
2.0164
-0.03714286
0.00138
1.42
2.0164
-0.03714286
0.00138
1.45
2.1025
-0.00714286
0.000051
1.52
2.3104
0.062857143
0.003951
1.56
2.4336
0.102857143
0.01058
1.58
2.4964
0.122857143
0.015094
1.60
2.56
0.142857143
0.020408
1.63
2.6569
0.172857143
0.02988
First and third quartiles
1.75
3.0625
0.292857143
0.085765
Q; = () • N
• 14 = 3.5 or 4th quartile
Ex = 20.4, N= 14
Ex = 30.0972
Ed = -0.04
Ed? = 0.371486
Standard deviation and variance
Q=1.36
Q = () .
* N
0.371486
Population variance - g? = Ed²
= 0.0265
14
• 14 = 10.5 or 11th quartile
Q = 1.58
Population standard deviation - o = Vo? = V0.0265 = 0.1628
• Range
Range = highest value – lowest value
0.3716
Sample variance - s² =
N-1
0.0286
14-1
= 1.75 – 1.06
Sample standard deviation - s =
V0.0286 = 0.1691
= 0.69

Transcribed Image Text:GWA (x)
x
d
d?
b. For female students
(Deviation from the
mean)
• Mean
1.4884
0.083016
1.22
-0.288125
Ex
1.24
1.5376
-0.268125
24.13
0.071891
=
1.508125
16
1.27
1.6129
-0.238125
0.056704
1.43
2.0449
-0.078125
0.006104
• Median
1.45
2.1025
-0.058125
0.003379
1.49
2.2201
-0.018125
0.000329
1.54+1.56
Med
1.55
1.49
2.2201
-0.018125
0.000329
2
1.54
2.3716
0.031875
0.001016
1.56
2.4336
0.051875
0.002691
Minimum and maximum values
1.56
2.4336
0.051875
0.002691
Min (x) = 1.22
Маx (х) — 1.78
1.58
2.4964
0.071875
0.005166
1.59
2.5281
0.081875
0.006704
1.59
1.64
2.5281
0.081875
0.006704
2.6896
0.131875
0.017391
First and third quartiles
1.70
2.89
0.191875
0.036816
Q1 = () • N
1.78
3.1684
0.271875
0.073916
Ex = 24.13, N = 16
Ex = 36.7659
Ed = -0.007
Ed = 0.374847
| • 16 = 4th quartile
Q1 = 1.43
Q3 = )
* N
• 16 = 12th quartile
= 1.59
• Standard deviation and variance
Range
Range = highest value – lowest value
= 1.78 – 1.22
Population variance - g² = Ed*
0.374847
= 0.0234
16
= 0.56
Population standard deviation - o =
0.0234 = 0.1530
Σα"
0.374847
• Interquartile range
Sample variance - s² =
0.0250
N-1
15-1
IQR = Qs – Q1
= 1.59 – 1.44 = 0.16
Sample standard deviation -s = Vs2 = V0.0249 = 0.1578
%3D
||
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