Question

The marks obtained by seven students in a test are: 36, 46, 70, 60, 20, 18, 30. What is the mean deviation of the data from the mean?

• A. 15.4
• B. 16
• C. 18
• D. 18.6

Hint:

For mean deviation, first calculate the mean, then find the absolute differences between each data point and the mean, and finally find the average of these differences.

Answer 1

The Correct Option is A

The mean deviation of a data set is the average of the absolute differences between each data point and the mean. The formula is: \[ \text{Mean Deviation} = \frac{1}{n} \sum |x_i - \bar{x}| \] Where: - \( x_i \) are the data points, - \( \bar{x} \) is the mean of the data, - \( n \) is the number of data points. The given data is: 36, 46, 70, 60, 20, 18, 30. First, find the mean: \[ \bar{x} = \frac{36 + 46 + 70 + 60 + 20 + 18 + 30}{7} = \frac{280}{7} = 40 \] Now, calculate the absolute differences from the mean: \[ |36 - 40| = 4, \quad |46 - 40| = 6, \quad |70 - 40| = 30, \quad |60 - 40| = 20, \quad |20 - 40| = 20, \quad |18 - 40| = 22, \] \[\quad |30 - 40| = 10 \] Sum of absolute differences: \[ 4 + 6 + 30 + 20 + 20 + 22 + 10 = 112 \] Now, calculate the mean deviation: \[ \text{Mean Deviation} = \frac{112}{7} = 15.4 \] Thus, the correct answer is 15.4.