1.
55, 56, 59, 60, 60, 60, 60, 62, 62, 62, 63, 65, 65, 70, 70, 70, 72, 80, 82, 85
Range of scores = 85 − 55 = 30 =85-55 =30 = 85 − 55 = 30
Number of classes = 7 =7 = 7
Class width = 30 7 = 5 =\dfrac{30}{7}=5 = 7 30 = 5
C l a s s l i m i t s C l a s s b o u n d a r i e s T a l l y F r e q u e n c y 53 − 57 52.5 − 57.5 ∣ ∣ 2 58 − 62 57.5 − 62.5 ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ 8 63 − 67 62.5 − 67.5 ∣ ∣ ∣ 3 68 − 72 67.5 − 72.5 ∣ ∣ ∣ ∣ 4 73 − 77 72.5 − 77.5 0 78 − 82 77.5 − 82.5 ∣ ∣ 2 83 − 87 82.5 − 87.5 ∣ 1 \begin{matrix}
\begin{alignedat}{2}
Class \\
limits
\end{alignedat} & \begin{alignedat}{2}
Class\ \ \ \ \ \ \\
boundaries
\end{alignedat} & Tally & Frequency \\
53-57 & 52.5-57.5 & || & 2 \\
58-62 & 57.5-62.5 & \cancel{|||||}\ ||| & 8 \\
63-67 & 62.5-67.5 & ||| & 3 \\
68-72 & 67.5 - 72.5 & |||| & 4 \\
73-77 & 72.5-77.5 & & 0 \\
78-82 & 77.5-82.5 & || & 2 \\
83-87 & 82.5-87.5 & | & 1
\end{matrix} Cl a ss l imi t s 53 − 57 58 − 62 63 − 67 68 − 72 73 − 77 78 − 82 83 − 87 Cl a ss b o u n d a r i es 52.5 − 57.5 57.5 − 62.5 62.5 − 67.5 67.5 − 72.5 72.5 − 77.5 77.5 − 82.5 82.5 − 87.5 T a ll y ∣∣ ∣∣∣∣∣ ∣∣∣ ∣∣∣ ∣∣∣∣ ∣∣ ∣ F re q u e n cy 2 8 3 4 0 2 1
2.
C l a s s l i m i t s F r e q u e n c y C u m u l a t i v e f r e q u e n c y 53 − 57 2 2 58 − 62 8 10 63 − 67 3 13 68 − 72 4 17 73 − 77 0 17 78 − 82 2 19 83 − 87 1 20 \begin{matrix}
\begin{alignedat}{2}
Class \\
limits
\end{alignedat} &\begin{alignedat}{2}
Frequency \\
\end{alignedat} & \begin{alignedat}{2}
Cumulative \\
frequency
\end{alignedat} \\
53-57 & 2 & 2 \\
58-62 & 8 & 10 \\
63-67 & 3 & 13 \\
68-72 & 4 & 17\\
73-77 & 0 & 17\\
78-82 & 2 & 19 \\
83-87 & 1 & 20
\end{matrix} Cl a ss l imi t s 53 − 57 58 − 62 63 − 67 68 − 72 73 − 77 78 − 82 83 − 87 F re q u e n cy 2 8 3 4 0 2 1 C u m u l a t i v e f re q u e n cy 2 10 13 17 17 19 20
3.
C l a s s l i m i t s F r e q u e n c y C u m u l a t i v e f r e q u e n c y P e r c e n t a g e C u m u l a t i v e p e r c e n t a g e 53 − 57 2 2 0.1 0.1 58 − 62 8 10 0.4 0.5 63 − 67 3 13 0.15 0.65 68 − 72 4 17 0.2 0.85 73 − 77 0 17 0 0.85 78 − 82 2 19 0.1 0.95 83 − 87 1 20 0.05 1 \begin{matrix}
\begin{alignedat}{2}
Class \\
limits
\end{alignedat} & Frequency & \begin{alignedat}{2}
Cumulative \\
frequency
\end{alignedat} & \begin{alignedat}{2}
Percentage \\
\end{alignedat} & \begin{alignedat}{2}
Cumulative \\
percentage
\end{alignedat} \\
53-57 & 2 & 2 & 0.1 & 0.1 \\
58-62 & 8 & 10 & 0.4 & 0.5 \\
63-67 & 3 & 13 & 0.15 & 0.65 \\
68-72 & 4 &17 & 0.2 & 0.85 \\
73-77 & 0 & 17 & 0 & 0.85 \\
78-82 & 2 & 19 & 0.1 & 0.95 \\
83-87 & 1 & 20 & 0.05 & 1
\end{matrix} Cl a ss l imi t s 53 − 57 58 − 62 63 − 67 68 − 72 73 − 77 78 − 82 83 − 87 F re q u e n cy 2 8 3 4 0 2 1 C u m u l a t i v e f re q u e n cy 2 10 13 17 17 19 20 P erce n t a g e 0.1 0.4 0.15 0.2 0 0.1 0.05 C u m u l a t i v e p erce n t a g e 0.1 0.5 0.65 0.85 0.85 0.95 1
4.
m e a n = 1 20 ( 55 + 56 + 59 + 4 ( 60 ) + 3 ( 62 ) + 63 mean=\dfrac{1}{20}(55+56+59+4(60)+3(62)+63 m e an = 20 1 ( 55 + 56 + 59 + 4 ( 60 ) + 3 ( 62 ) + 63
+ 2 ( 65 ) + 3 ( 70 ) + 72 + 80 + 82 + 85 ) = 65.9 +2(65)+3(70)+72+80+82+85)=65.9 + 2 ( 65 ) + 3 ( 70 ) + 72 + 80 + 82 + 85 ) = 65.9
m o d e = 60 , appeared 4 times mode=60, \text{appeared 4 times} m o d e = 60 , appeared 4 times
m e d i a n = 62 + 63 2 = 62.5 median=\dfrac{62+63}{2}=62.5 m e d ian = 2 62 + 63 = 62.5
Comments