If the mean deviation about median for the number 3, 5, 7, 2k, 12, 16, 21, 24 arranged in the ascending order, is 6 then the median is

Complete Solution:

Since there are 8 numbers, the median is the average of the 4th and 5th values in the ordered list:

• The 4th value is 2k
• The 5th value is 12

Thus, the median is:

Median = (2k + 12) / 2

The mean deviation about the median is calculated by taking the absolute differences of each value from the median and averaging them.

Mean Deviation (M.D.) formula:

M.D. = (∑ |x_i - Median|) / n

• x_i represents each value in the dataset
• n = 8 (total number of values)
• The mean deviation is given as 6

Let’s denote the median as M:

M = (2k + 12) / 2

The mean deviation is given as:

(|3 - M| + |5 - M| + |7 - M| + |2k - M| + |12 - M| + |16 - M| + |21 - M| + |24 - M|) / 8 = 6

Substitute the value of M:

M = 11

To determine k:

(2k + 12) / 2 = 11

Multiply both sides by 2:

2k + 12 = 22

Subtract 12 from both sides:

2k = 10

Divide by 2:

k = 5

If k = 5, the median becomes:

M = 11

Final Answer:

The median of the dataset is 11.