1.
Mean = 97.1 + 97.8 + 98.0 + 98.9 + 99.5 + 96.3 6 = 97.93 =\frac{97.1+97.8+98.0+98.9+99.5+96.3}{6}=97.93 = 6 97.1 + 97.8 + 98.0 + 98.9 + 99.5 + 96.3 = 97.93
Standard deviation = ∑ ( x − x ˉ ) 2 n − 1 \sqrt{\frac{\sum(x-\bar x)^2}{n-1}} n − 1 ∑ ( x − x ˉ ) 2
From the given data, the standard deviation is:
S = 1.16 S=1.16 S = 1.16
The data: 96.3, 97.1, 97.8, 98.0, 98.9, 99.5
First Quartile(Q1) = ( ( n + 1 ) / 4 ) t h =((n+1)/4)^{th} = (( n + 1 ) /4 ) t h = 7 / 4 = 1 s t t e r m = 96.9 =7/4=1^{st}\hspace{3pt}term=96.9 = 7/4 = 1 s t t er m = 96.9
Second Quartile(Q2)= = ( ( n + 1 ) / 2 ) t h t e r m = 97.9 ==((n+1)/2)^{th}\hspace{3pt} term=97.9 == (( n + 1 ) /2 ) t h t er m = 97.9
Third Quartile(Q3) = ( 3 ( n + 1 ) / 4 ) t h t e r m = 99.05 =(3(n+1)/4)^{th}\hspace{3pt}term=99.05 = ( 3 ( n + 1 ) /4 ) t h t er m = 99.05
Box and Whisker Plot:
Stem and Leaf Diagram:
2.
Mean = 98.4 + 98.5 + 98.1 + 100.8 + 98.6 + 98.2 6 = 98.77 =\frac{98.4+98.5+98.1+100.8+98.6+98.2}{6}=98.77 = 6 98.4 + 98.5 + 98.1 + 100.8 + 98.6 + 98.2 = 98.77
Standard deviation = ∑ ( x − x ˉ ) 2 n − 1 \sqrt{\frac{\sum(x-\bar x)^2}{n-1}} n − 1 ∑ ( x − x ˉ ) 2
From the given data, the standard deviation is:
S = 1.01 S=1.01 S = 1.01
The data: 98.1,98.2,98.4,98.5,98.6,100.8
First Quartile(Q1) = ( ( n + 1 ) / 4 ) t h =((n+1)/4)^{th} = (( n + 1 ) /4 ) t h = 7 / 4 = 1 s t t e r m = 98.175 =7/4=1^{st}\hspace{3pt}term=98.175 = 7/4 = 1 s t t er m = 98.175
Second Quartile(Q2)= = ( ( n + 1 ) / 2 ) t h t e r m = 98.45 ==((n+1)/2)^{th}\hspace{3pt} term=98.45 == (( n + 1 ) /2 ) t h t er m = 98.45
Third Quartile(Q3) = ( 3 ( n + 1 ) / 4 ) t h t e r m = 99.15 =(3(n+1)/4)^{th}\hspace{3pt}term=99.15 = ( 3 ( n + 1 ) /4 ) t h t er m = 99.15
Box and Whisker Plot:
Stem and Leaf Diagram:
3.
Mean = 98.52 =98.52 = 98.52
Standard deviation = ∑ ( x − x ˉ ) 2 n − 1 \sqrt{\frac{\sum(x-\bar x)^2}{n-1}} n − 1 ∑ ( x − x ˉ ) 2
From the given data, the standard deviation is:
S = 0.81 S=0.81 S = 0.81
The data: 97.4,97.6,98.8,99.0,99.0,99.3
First Quartile(Q1) = ( ( n + 1 ) / 4 ) t h =((n+1)/4)^{th} = (( n + 1 ) /4 ) t h = 7 / 4 = 1 s t t e r m = 97.55 =7/4=1^{st}\hspace{3pt}term=97.55 = 7/4 = 1 s t t er m = 97.55
Second Quartile(Q2)= = ( ( n + 1 ) / 2 ) t h t e r m = 98.9 ==((n+1)/2)^{th}\hspace{3pt} term=98.9 == (( n + 1 ) /2 ) t h t er m = 98.9
Third Quartile(Q3) = ( 3 ( n + 1 ) / 4 ) t h t e r m = 99.075 =(3(n+1)/4)^{th}\hspace{3pt}term=99.075 = ( 3 ( n + 1 ) /4 ) t h t er m = 99.075
Box and Whisker Plot:
Stem and Leaf Diagram:
4.
Mean = 97.7 =97.7 = 97.7
Standard deviation = ∑ ( x − x ˉ ) 2 n − 1 \sqrt{\frac{\sum(x-\bar x)^2}{n-1}} n − 1 ∑ ( x − x ˉ ) 2
From the given data, the standard deviation is:
S = 0.73 S=0.73 S = 0.73
The data: 96.4,97.4,97.8,98.0,98.1,98.5
First Quartile(Q1) = ( ( n + 1 ) / 4 ) t h =((n+1)/4)^{th} = (( n + 1 ) /4 ) t h = 7 / 4 = 1 s t t e r m = 97.15 =7/4=1^{st}\hspace{3pt}term=97.15 = 7/4 = 1 s t t er m = 97.15
Second Quartile(Q2)= = ( ( n + 1 ) / 2 ) t h t e r m = 97.9 ==((n+1)/2)^{th}\hspace{3pt} term=97.9 == (( n + 1 ) /2 ) t h t er m = 97.9
Third Quartile(Q3) = ( 3 ( n + 1 ) / 4 ) t h t e r m = 98.2 =(3(n+1)/4)^{th}\hspace{3pt}term=98.2 = ( 3 ( n + 1 ) /4 ) t h t er m = 98.2
Box and Whisker Plot:
Stem and Leaf Diagram:
5.
Mean = 98.38 =98.38 = 98.38
Standard deviation = ∑ ( x − x ˉ ) 2 n − 1 \sqrt{\frac{\sum(x-\bar x)^2}{n-1}} n − 1 ∑ ( x − x ˉ ) 2
From the given data, the standard deviation is:
S = 0.47 S=0.47 S = 0.47
The data: 97.6,98.2,98.2,98.7,98.8,98.8
First Quartile(Q1) = ( ( n + 1 ) / 4 ) t h =((n+1)/4)^{th} = (( n + 1 ) /4 ) t h = 7 / 4 = 1 s t t e r m = 98.05 =7/4=1^{st}\hspace{3pt}term=98.05 = 7/4 = 1 s t t er m = 98.05
Second Quartile(Q2)= = ( ( n + 1 ) / 2 ) t h t e r m = 98.45 ==((n+1)/2)^{th}\hspace{3pt} term=98.45 == (( n + 1 ) /2 ) t h t er m = 98.45
Third Quartile(Q3) = ( 3 ( n + 1 ) / 4 ) t h t e r m = 98.8 =(3(n+1)/4)^{th}\hspace{3pt}term=98.8 = ( 3 ( n + 1 ) /4 ) t h t er m = 98.8
Box and Whisker Plot:
Stem and Leaf Diagram:
#339914 on Dec 2023
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