What is the mean deviation of eight observations? $6, 7, 10, 12, 13, 4, 8, 12$
Mean Deviation Calculation Steps
Follow these steps to find the mean deviation for the given observations.
Observations Ordered
First, arrange the eight observations in ascending order:
4, 6, 7, 8, 10, 12, 12, 13
Mean Calculation
Next, calculate the mean ($\bar{x}$) of the observations.
Sum of observations = $4 + 6 + 7 + 8 + 10 + 12 + 12 + 13 = 72$
Number of observations ($n$) = 8
Mean ($\bar{x}$) = $\frac{\sum x_i}{n} = \frac{72}{8} = 9$
Absolute Deviations from Mean
Calculate the absolute difference between each observation and the mean (9).
| Observation ($x_i$) | Absolute Deviation ($|x_i - \bar{x}|$) |
| 4 | $|4 - 9| = 5$ |
| 6 | $|6 - 9| = 3$ |
| 7 | $|7 - 9| = 2$ |
| 8 | $|8 - 9| = 1$ |
| 10 | $|10 - 9| = 1$ |
| 12 | $|12 - 9| = 3$ |
| 12 | $|12 - 9| = 3$ |
| 13 | $|13 - 9| = 4$ |
Mean Deviation Calculation
Finally, calculate the mean deviation (MD) by averaging the absolute deviations.
Sum of absolute deviations = $5 + 3 + 2 + 1 + 1 + 3 + 3 + 4 = 22$
Mean Deviation (MD) = $\frac{\sum |x_i - \bar{x}|}{n} = \frac{22}{8} = 2.75$
Conclusion
The mean deviation of the eight observations is 2.75.
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Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
Find the mean of first 5 two-digit multiples of 4.
