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**Mean Deviation**

**Mean deviation**or

**average deviation**is defined as the arithmetic mean of the deviations of the items from mean or median or mode. Since median is the central point of any distribution, mean deviation from median generally gives the best result among the average deviations. Since mode is ill defined, mean deviation from mode will generally be not used.

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__Individual Series__**:**

__Individual Series__

In case of individual series, mean
deviation is calculated as follows:

Where A = mean or median or mode and |x – A| is
modulus or absolute value of x – A. That is magnitude of (x – A) or value of
deviation taken from average A ignoring the negative sign.

###
__Discrete and Continuous Series__**:**

__Discrete and Continuous Series__

In case of discrete and continuous series the mean
deviation can be calculated by the formula,

In case of continuous distribution, x is taken as
the mid-point of corresponding class.

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**Coefficient of Mean Deviation**

The coefficient of mean deviation is given by the
formula,

Where A is the average from which the mean
deviation is calculated.

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*Workout
Examples*

*Workout Examples*

*Example 1: Calculate the mean deviation and its coefficient from mean and median of the following series.*

*24, 28, 29, 33, 36, 35, 25*

*Solution:*

*Here,*

*Arranging the data in ascending order,*

*Data: 24, 25, 28, 29, 33, 35, 36*

*No. of data (N) = 7*

*Calculation of Mean Deviation*M.D. from mean |
M.D. from median |
||||

x |
x – A |
|x – A| |
x |
x – A |
|x – A| |

24252829333536 |
-6-5-2-1356 |
6521356 |
24252829333536 |
-5-4-10467 |
5410467 |

∑|x – A| = 28 |
∑|x – A| = 27 |

*Now,*

*Example 2: Calculate the mean deviation from median of the following frequency table. Also find its coefficient.*

Height (cm) |
10 |
20 |
30 |
40 |
50 |
60 |

No. of plants |
2 |
3 |
9 |
21 |
11 |
5 |

*Solution:*

*Here,*

*Calculation of Mean Deviation*x |
f |
cf |
|x – A| |
f|x – A| |

102030405060 |
23921115 |
2514354651 |
30201001020 |
6060900110100 |

N = 51 |
420 |

*Now,*

*No. of data (N) = 51*

*Hence, mean deviation from median is 8.235 and its coefficient is 0.205.*

*Example 3: Find the mean deviation from mean and its coefficient.*

Marks |
10-20 |
20-30 |
30-40 |
40-50 |
50-60 |
60-70 |
70-80 |

No. of Students |
4 |
7 |
9 |
18 |
12 |
7 |
3 |

*Solution:*

*Here,*

Marks |
Frequency (f) |
Mid-value (x) |
fx |
|x – A| |
f|x – A| |

10-2020-3030-4040-5050-6060-7070-80 |
479181273 |
15253545556575 |
60175315810660455225 |
3020100102030 |
12014090012014090 |

N = 60 |
2700 |
700 |

Here, total no. of data (N) = 60Here, total no. of data (N) = 60

*Hence, mean deviation = 11.667 and its coefficient = 0.259.*

*You can comment your questions or problems regarding*

**mean deviation**here.
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