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

Solution

Maths sir · 4 steps

The median pins a and b below 170. The deviation sum then gives a + b, and that is all you need.

1. Use the median. Sorted, the known values are 125, 170, 190, 210, 230. For 170 to be the 4th of 7 values, exactly three values must lie on each side of it. Three known values (190, 210, 230) are already above 170, so both a ≤ 170 and b ≤ 170.
2. Deviation about median. The known values give 0 + 45 + 60 + 20 + 40 = 165. Since a, b ≤ 170, they add (170 - a) + (170 - b) = 340 - (a+b). Setting the total equal to 7 × 205/7 = 205 gives 505 - (a+b) = 205, so a + b = 300.

   x̄ = (170+125+230+190+210+300)/7 = 1225/7 = 175

3. Deviation about mean. The known values give 5 + 50 + 55 + 15 + 35 = 160. Both a and b are below 175, so they add (175 - a) + (175 - b) = 350 - 300 = 50. The total is 210.
4. So. The mean deviation about the mean is 210/7 = 30, which is option (c).

The idea to keep. You do not need a and b separately. Once you know which side of the centre each one lies on, their absolute deviations only need their sum.

Answer from the NTA final answer key. Solution by PrepWiser.