Question

Let the median and the mean deviation about the median of 7 observation 170, 125, 230, 190, 210, a, b be 170 and $\frac{205}{7}$respectively. Then the mean deviation about the mean of these 7 observations is :

• A. 31
• B. 28
• C. 30
• D. 32

Answer 1

Answer: (C)

30

Answer 2

Given that the median is 170, the observations are arranged as:

125, a, b, 170, 190, 210, 230

The mean deviation about the median is given by:

$\frac{0 + |45| + |60| + |20| + |40| + |170 - a| + |170 - b|}{7} = \frac{205}{7}$

From this, we find:

$|170 - a| + |170 - b| = 300 \implies a + b = 300$

Now, the mean of the observations is:

$\text{Mean} = \frac{125 + a + b + 170 + 190 + 210 + 230}{7} = \frac{125 + 300 + 170 + 190 + 210 + 230}{7} = 175$

The mean deviation about the mean is:

$\frac{|125 - 175| + |a - 175| + |b - 175| + |170 - 175| + |190 - 175| + |210 - 175| + |230 - 175|}{7}$

Simplifying:

$\frac{50 + |a - 175| + |b - 175| + 5 + 15 + 35 + 55}{7} = 30$