Mean Deviation Calculation

To find the mean deviation from the mean for the data set {58, 65, 42, 66, 49, 59, 44, 45, 62, 60}, follow these steps:

Mean Calculation for Data

First, calculate the mean ($\bar{x}$) of the data.

Sum = $58 + 65 + 42 + 66 + 49 + 59 + 44 + 45 + 62 + 60 = 550$

Number of data points ($n$) = 10

Mean ($\bar{x}$) = $\frac{\sum x_i}{n} = \frac{550}{10} = 55$

Absolute Deviations from Mean

Next, find the absolute difference between each data point ($x_i$) and the mean ($\bar{x}=55$).

• $|58 - 55| = 3$
• $|65 - 55| = 10$
• $|42 - 55| = 13$
• $|66 - 55| = 11$
• $|49 - 55| = 6$
• $|59 - 55| = 4$
• $|44 - 55| = 11$
• $|45 - 55| = 10$
• $|62 - 55| = 7$
• $|60 - 55| = 5$

Sum of absolute deviations = $3 + 10 + 13 + 11 + 6 + 4 + 11 + 10 + 7 + 5 = 80$

Mean Deviation Calculation

Finally, calculate the mean deviation (MD) by dividing the sum of absolute deviations by the number of data points ($n$).

Mean Deviation (MD) = $\frac{\sum |x_i - \bar{x}|}{n} = \frac{80}{10} = 8$

Final Answer

The mean deviation from the mean for the data set is 8.