Questions: Find the relative average deviation of the following data in %: (report 3 decimal places) 6.37, 6.45, 5.4, 6.56, 5.37, 5.89, 4.5

Solution Steps

To find the relative average deviation of the given data set, we first calculate the mean of the data. Then, we find the absolute deviation of each data point from the mean. The average of these absolute deviations is calculated next. Finally, the relative average deviation is obtained by dividing the average deviation by the mean and multiplying by 100 to express it as a percentage.

To find the mean of the data set, sum all the data points and divide by the number of data points. The data set is \([6.37, 6.45, 5.4, 6.56, 5.37, 5.89, 4.5]\).

\[ \text{Mean} = \frac{6.37 + 6.45 + 5.4 + 6.56 + 5.37 + 5.89 + 4.5}{7} = 5.7914 \]

Calculate the absolute deviation of each data point from the mean:

\[ \begin{align_} |6.37 - 5.7914| & = 0.5786 \\ |6.45 - 5.7914| & = 0.6586 \\ |5.4 - 5.7914| & = 0.3914 \\ |6.56 - 5.7914| & = 0.7686 \\ |5.37 - 5.7914| & = 0.4214 \\ |5.89 - 5.7914| & = 0.0986 \\ |4.5 - 5.7914| & = 1.2914 \\ \end{align_} \]

Find the average of the absolute deviations:

\[ \text{Average Deviation} = \frac{0.5786 + 0.6586 + 0.3914 + 0.7686 + 0.4214 + 0.0986 + 1.2914}{7} = 0.6012 \]

The relative average deviation is calculated by dividing the average deviation by the mean and multiplying by 100 to express it as a percentage:

\[ \text{Relative Average Deviation} = \left(\frac{0.6012}{5.7914}\right) \times 100 = 10.381\% \]

Final Answer