Find the mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17.
Solution and Explanation
The given data is
4, 7, 8, 9, 10, 12, 13, 17
Mean of the data, \(\bar{x}=\frac{4+7+8+10+12+13+17}{8}=\frac{80}{8}=10\)
The deviations of the respective observations from the mean \(\bar{x},i.e.x_i-\bar{x},\) are:
6, 3, 2, 1, 0, 2, 3, 7
The absolute values of the deviations, i.e. \(|x_i-\bar{x}|\), are:
6, 3, 2, 1, 0, 2, 3, 7
The required mean deviation about the mean is
M.D.\(\bar{x}=\frac{\sum_{i=1}^{8}|x_i-\bar{x}|}{8}=\frac{6+3+2+1+0+2+3+7}{8}\)
\(=\frac{24}{8}=3\)
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Questions Asked in CBSE Class XI exam
Give reasons for the following.
(i) King Tut’s body has been subjected to repeated scrutiny.
(ii) Howard Carter’s investigation was resented.
(iii) Carter had to chisel away the solidified resins to raise the king’s remains.
(iv) Tut’s body was buried along with gilded treasures.
(v) The boy king changed his name from Tutankhaten to Tutankhamun.- CBSE Class XI
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Concepts Used:
Mean Deviation
A statistical measure that is used to calculate the average deviation from the mean value of the given data set is called the mean deviation.
The Formula for Mean Deviation:
The mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
- Σ represents the addition of values
- X represents each value in the data set
- µ represents the mean of the data set
- N represents the number of data values
Grouping of data is very much possible in two ways:
- Discrete Frequency Distribution
- Continuous Frequency Distribution