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?

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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?

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: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
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
||
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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