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.
Similar Questions
- The following observations are arranged in ascending order. If the median of the data is 19, then find the value of x.
6, 9, 15, x + 4, x + 8, x + 12, 30, 32 - The marks scored by 10 students are given below.
17, 19, 12, 20, 19, 14, 15, 18, 19, 14
The mode of the given data is: - Let a set S = {1, 2, 2, 3, 3, 3, 4, 4, 4, 4}. Then the value of $4 \times \text{mean} + 2 \times \text{mode} - 8 \times \text{median}$ is:
- The weights (in kg) of 7 men are 64, 63, 62, 65, 67, 66 and 61. The median weight is:
- Which of the following CANNOT take a negative value?
- The given data is arranged in ascending order and its median is 17. Find the value of $x$.
$8, 10, 12, 15, x, x + 2, 20, 25, 30, 32$ - Find the sum of the mean, median and mode of the given data.
$9, 35, 20, 25, 25, 15, 25$ - In the given data if 30 is replaced by 100 then find the difference of the two medians.
80, 90, 40, 30, 20, 10, 70, 60, 50 - Find the mean height of persons from the following data.
Height (cm) Number of persons 120 3 130 4 140 5 150 6 160 2 - If the mean of the following data is k, then find the value of k.
Value 3 2 k 4 5 Frequency k 2k 3k 4k 5k
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.
What will be the difference between mean and median of the given data?
21, 11, 27, 8, 5, 12, 7, 23, 3, 14, 9, 19Find 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
