The document discusses different methods for calculating the arithmetic mean or simple mean of a data set. It defines the arithmetic mean as the sum of all observations divided by the total number of observations. It then presents three main methods for calculating the mean: 1) the coding method using an assumed mean, 2) the scaling method using an assumed mean and unit of measurement, and 3) the weighted mean which incorporates weights for each observation. Examples are provided to demonstrate calculating the mean for raw data sets, grouped data sets, and weighted data sets.

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2. How To calculate Arithmetic Mean or Simple Mean?
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3. Arithmetic Mean
Arithmetic mea is a value obtained by dividing
the sum of all the observations by their number.
Or
If X1, X2, X3, X4 . . . . . . . Xn are n observation of a
variable X, then the arithmetic mean, denoted
by x is defined as
𝑋 =
X1+X2+X3+X4 + . . . . . . +Xn
𝑛
=
𝑋𝑖
𝑛
Where i= 1, 2 ,3,……….n
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4. 1. Coding method of calculating Mean
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𝑋 = a +
𝐷
𝑛 Where D = X-a Also a is know as assumed mean
2. Scaling Method of calculating mean
𝑋 = a +
ℎ 𝑈
𝑛 Where U = X-a/h
Also a is know as assumed mean and h is the unit of measurement.
3. Weighted Arithmetic Mean
𝑋 =
X1W1+X2W2+X3W3+X4W4+ . . . . . . +XnW 𝑛
W1+W2+W3+W4+ . . . . . . +W 𝑛
=
𝑋𝑖𝑊𝑖
𝑊𝑖

5. Example 1
X
67
72
68
70
65
68
75
63
𝑋= 548
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D=X-70
-3
2
-2
0
-5
-2
5
-7
𝐷= -12
𝑋 =
𝑋𝑖
𝑛
=
548
8
= 68.5
𝑋 = a +
𝐷
𝑛
𝑋 = 70 +
−12
8
= 68.5

6. Example 2 (Weighted Mean)
Item X Weights XW
Food 290 7.5 2175
Rent 54 2 108
Clothing 98 1.5 147
Fuel 75 1 75
Misc. 75 0.5 37.5
Sums 𝑊=12.5 𝑋𝑊=2542.5
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X =
𝑋𝑖𝑊𝑖
𝑊𝑖
=
𝟐𝟓𝟒𝟐.𝟓
𝟏𝟐.𝟓
= 203.4

7. Grouped Data
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𝑋 =
𝒇𝑿𝒊
𝑓
𝑿 = 𝐚 +
𝒇𝑫
𝒇
𝑋 = a +
ℎ 𝑓𝑈
𝑓
Coding method of calculating Mean
Simple Mean
Scaling Method of calculating mean

8. Example 3(Grouped Data)
Groups f
35-39 13
40-44 15
45-49 28
50-54 17
55-59 12
60-64 10
65-69 5
Sums 𝑓=100
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X
37
42
47
52
57
62
67
X= (Upper class Boundary +Lower Class Boundary) /2
fX
481
630
1316
884
684
620
335
𝒇𝑿𝒊 =4950
U= X-47/5
-2
-1
0
1
2
3
4
fU
-26
-15
0
17
24
30
20
50
𝑋 =
𝒇𝑿𝒊
𝑓
=
4950
100
= 49.5 𝑋 = a +
ℎ 𝑓𝑈
𝑓
= 47 +
5(50)
100
= 49.5
𝑿 = 𝐚 +
𝒇𝑫
𝒇
= 47+
250
100
= 49.5
D=X-47
-10
-5
0
5
10
15
20
35
fD
-130
-75
0
85
120
150
100
250

9. Next Video
How to Calculate Median?
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