The Mean Deviation Formula

For a set of data x₁, x₂, x₃, ..., x_n which has an mean of x̄ and absolute value of deviation per data | x₁ - x̄ |, | x₂ - x̄ |, | x₃ - x̄ |, ..., | x_n - x̄ | summed then divided by the amount of data then obtained the mean deviation formulated as follows :

The Mean Deviation Formula

RD = 1/n ∑ | x_i - x̄ |

Information :

x_i = x₁, x₂, x₃, ..., x_n
x̄ = Mean of data
n = Amount frequencies of data
∑ = Sigma (number symbol)
RD = Mean deviation value

Example :

Determine the mean deviation of 6, 4, 8, 10, 11, 10, 7 !

Answer :

x₁ = 4

x₂ = 6

x₃ = 7

x₄ = 8

x₅ = 10

x₆ = 10

x₇ = 11

n = 7

x̄ = (4 + 6 + 7 + 8 + 10 + 10 + 11) / 7

x̄ = 56 / 7

x̄ = 8

∑ | x_i - x̄ |  = | x₁ - x̄ | + | x₂ - x̄ | + | x₃ - x̄ | + | x₄ - x̄ | + | x₅ - x̄ | + | x₆ - x̄ | + | x₇ - x̄ |

∑ | x_i - x̄ |  = | 4 - 8 | + | 6 - 8 | + | 7 - 8 | + | 8 - 8 | + | 10 - 8 | + | 10 - 8 | + | 11 - 8 |

∑ | x_i - x̄ |  = | -4 | + | -2 | + | -1 | + | 0 | + | 2 | + | 2 | + | 3 |

∑ | x_i - x̄ |  = 4 + 2 + 1 + 0 + 2 + 2 + 3

∑ | x_i - x̄ |  = 14

RD = 1/n ∑ | x_i - x̄ |
RD = 1/7 (14)
RD = 14 / 7
RD = 2

So the mean deviation value of 6, 4, 8, 10, 11, 10, 7 is 2

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Referensi :

• Book math group sales and accounting essay To'ali class 12

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