Question

calculate mean deviation and its Coefficient from median from the following data 10,80,70,20,40,55,75​

Answer 1

Answer: Median item $=\frac{\mathrm{N}}{2}=\frac{20}{2}=10$ th item which lies in the class interval$29.5-39.5$

Here, $l_1=$lower limit of median class $=29.5$

c. $f=$ cumulative frequency of preceding median class $=7$

$f=$frequency of median class $=6$

$\mathrm{h}= class size =10$

Median, $M=l_1+\frac{\frac{N}{2}-c . f}{f} \times i$

$=29.5+\frac{10-7}{6} \times 10$

$=34.5$

Mean deviation, $M . D_M=\frac{\sum f|D|}{N}=\frac{190}{20}=9.5$

Coefficient of $M . D_M=\frac{M \cdot D_M}{M}=\frac{9.5}{34.5}=0.275$

Explanation:

Step :1 Coefficient of Mean Deviation = Mean Deviation Median = 14. 46 31 = 0. 466. Mean Deviation from Median = M D M = f d M f = 1446 100 = 14. 46.

By using the formula$|xiM|n,$ the mean deviation from the median is computed. Put the median value into the calculation to get the mean deviation from the median.

Step:2 The median and Range/4 or Range/6 are frequently used in place of the mean and standard deviation, respectively. The use of the median to replace mean values and determine when range-formulas are suitable, however, has not been demonstrated.

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