JEE Mathematics 2024 Question with Solution

Given: The median of the $7$ observations is $170$ and the mean deviation about the median is $\frac{205}{7}$.

Find: The mean deviation about the mean.

Arrange the observations in ascending order using the median condition:

Using mean deviation about median $170$,

So,

From the ordering, $a,b \le 170$, hence

Now the mean is

Substituting $a+b=300$,

The mean deviation about the mean $175$ is

Since the observations become $125,130,170,170,190,210,230$, this is

Therefore, the mean deviation about the mean is $30$. The correct option is C.

Given: Observations are $170, 125, 230, 190, 210, a, b$. Median is $170$ and mean deviation about median is $\frac{205}{7}$.

Find: Mean deviation about the mean.

Since there are $7$ observations, the median is the 4th observation after arranging them in ascending order. Hence the ordered data can be written as

after determining the unknown values.

Use the mean deviation about median:

This gives

which is satisfied, so the unknown value below $170$ is $130$ and the other is $170$.

Now compute the mean:

Mean deviation about the mean $175$ is

Therefore, the mean deviation about the mean is $30$.