Write down the mathematical formula to find mean of a grouped data
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Write down the mathematical formula to find mean of a grouped data
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To calculate the mean of grouped data, the first step is to determine the midpoint (also called a class mark) of each interval, or class. These midpoints must then be multiplied by the frequencies of the corresponding classes. The sum of the products divided by the total number of values will be the value of the mean.
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Step-by-step explanation:
. Mean, Median and Mode for grouped data example ( Enter your problem )( Enter your problem )
Formula & Examples
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Geometric mean, Harmonic mean
Mean deviation, Quartile deviation, Decile deviation, Percentile deviation
2. Quartiles, Deciles and Percentiles
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1. Formula & Examples
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Formula
1. Mean
ˉ
x
=
∑fx
n
2. Median M=L+
n
2
-cf
f
⋅c
3. Mode Z=L+(
f1-f0
2⋅f1-f0-f2
)⋅c
Examples
1. Calculate Mean, Median, Mode from the following grouped data
Class Frequency
2 - 4 3
4 - 6 4
6 - 8 2
8 - 10 1
Solution:
Class
(1) Frequency (f)
(2) Mid value (x)
(3) f⋅x
(4)=(2)×(3) cf
(6)
2-4 3 3 3=
2+4
2
9 9=3×3
(4)=(2)×(3) 3 3=0+3
(6)=Previous (6)+(2)
4-6 4 5 5=
4+6
2
20 20=4×5
(4)=(2)×(3) 7 7=3+4
(6)=Previous (6)+(2)
6-8 2 7 7=
6+8
2
14 14=2×7
(4)=(2)×(3) 9 9=7+2
(6)=Previous (6)+(2)
8-10 1 9 9=
8+10
2
9 9=1×9
(4)=(2)×(3) 10 10=9+1
(6)=Previous (6)+(2)
--- --- --- --- ---
-- n=10 -- ∑f⋅x=52 --
Mean
ˉ
x
=
∑fx
n
=
52
10
=5.2
To find Median Class
= value of (
n
2
)th observation
= value of (
10
2
)th observation
= value of 5th observation
From the column of cumulative frequency cf, we find that the 5th observation lies in the class 4-6.
∴ The median class is 4-6.
Now,
∴L=lower boundary point of median class =4
∴n=Total frequency =10
∴cf=Cumulative frequency of the class preceding the median class =3
∴f=Frequency of the median class =4
∴c=class length of median class =2
Median M=L+
n
2
-cf
f
⋅c
=4+
5-3
4
⋅2
=4+
2
4
⋅2
=4+1
=5
To find Mode Class
Here, maximum frequency is 4.
∴ The mode class is 4-6.
∴L=lower boundary point of mode class =4
∴f1= frequency of the mode class =4
∴f0= frequency of the preceding class =3
∴f2= frequency of the succedding class =2
∴c= class length of mode class =2
Z=L+(
f1-f0
2⋅f1-f0-f2
)⋅c
=4+(
4-3
2⋅4-3-2
)⋅2
=4+(
1
3
)⋅2
=4+0.6667
=4.6667
2. Calculate Mean, Median, Mode from the following grouped data
X Frequency
0 1
1 5
2 10
3 6
4 3
Solution:
x
(1) Frequency (f)
(2) f⋅x
(3)=(2)×(1) cf
(5)
0 1 0 0=1×0
(3)=(2)×(1) 1 1=0+1
(5)=Previous (5)+(2)
1 5 5 5=5×1
(3)=(2)×(1) 6 6=1+5
(5)=Previous (5)+(2)
2 10 20 20=10×2
(3)=(2)×(1) 16 16=6+10
(5)=Previous (5)+(2)
3 6 18 18=6×3
(3)=(2)×(1) 22 22=16+6
(5)=Previous (5)+(2)
4 3 12 12=3×4
(3)=(2)×(1) 25 25=22+3
(5)=Previous (5)+(2)
--- --- --- ---
n=25 ∑f⋅x=55 --
Mean
ˉ
x
=
∑fx
n
=
55
25
=2.2
Median :
M = value of (
n
2
)th observation
= value of (
25
2
)th observation
= value of 12th observation
From the column of cumulative frequency cf, we find that the 12th observation is 2.
Hence, the median of the data is 2.
Mode :
the frequency of observation 2 is maximum (10)
∴Z=2
This material is intended as a summary. Use your textbook for detail explanation.
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