Correct Answer - Option 2 : 4.7
Concept:
Median: The data should be arranged in order from least to greatest. If there is an odd number of items in the data set, then the median is the middlemost number.
Mean deviation about the median = \(\rm \sum_{i=1}^n\frac{|x_i-M|}{n}\), where M = median
Calculation:
Given numbers: 7, 5, 4, 3, 10, 16, 19
Total numbers = n = 7
After arranging in order from least to greatest, we get
3, 4, 5, 7, 10, 16, 19
Median = middlemost number = 7
We know that, the mean deviation about the median = \(\rm \sum_{i=1}^n\frac{|x_i-M|}{n}\)
\(\rm = \frac{|3 - 7| + |4 - 7| + |5 - 7| +|7 - 7| +|10 - 7| +|16 - 7| +|19 - 7|}{7}\)
\(\rm = \frac{4 + 3 + 2 + 0+3+9+12}{7}=\frac{33}{7}\)
= 4.7
Hence, option (2) is correct.
