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Calculate the mean deviation from the mean of the distribution below
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Step-by-step solution
5 stepsTo calculate the mean deviation from the mean, we'll use the formula provided: .
First, we need to find the class mark () for each class, then calculate the mean (), and finally apply the mean deviation formula.
Assumption: For the class "10-10", we will take the class mark () as 10. For the other classes, the class mark is the midpoint of the interval.
Here's a table with the necessary calculations: | Class | Freq (f) | Class Mark (x) | | | | | :------ | :------- | :------------- | :----- | :-------------- | :--------------- | | 10-10 | 12 | 10 | 120 | 19.32 | 231.84 | | 10-20 | 25 | 15 | 375 | 14.32 | 358.00 | | 20-30 | 32 | 25 | 800 | 4.32 | 138.24 | | 30-40 | 25 | 35 | 875 | 5.68 | 142.00 | | 40-50 | 21 | 45 | 945 | 15.68 | 329.28 | | 50-60 | 10 | 55 | 550 | 25.68 | 256.80 | | Total | | | | | |
Calculate the total frequency () and the sum of ().
Calculate the mean ().
Calculate the absolute deviation for each class mark.
For :
For :
For :
For :
For :
For :Calculate for each class and sum them ().
Calculate the Mean Deviation (MD).
Rounding to two decimal places:
The mean deviation from the mean is .
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