Solution:

Given, Mode = 16 and Arithmetic mean = 20

To find: Median

Let's assume the number of observations as ‘n’.

Mode:

The mode is the observation that occurs most frequently in the given data set.

Given, mode = 16

Arithmetic Mean:

The arithmetic mean is the sum of all observations divided by the total number of observations.

Given, arithmetic mean = 20

Mean = Sum of all observations / n

20 = Sum of all observations / n

Sum of all observations = 20n

Median:

The median is the middle observation in the given data set when arranged in ascending or descending order.

Let's assume that the observations are arranged in ascending order.

Now, we need to use the formula to find the median,

Median = [(n + 1) / 2]th observation

We know that the mode is 16 and the sum of all observations is 20n.

Let’s assume that the mode occurs ‘m’ number of times.

So, the sum of all observations will be:

Sum of all observations = 16m + (20n - 16m) = 20n

20n - 16m = Sum of remaining observations

Also, we know that the arithmetic mean is 20.

So, the sum of all observations will be:

Sum of all observations = 20n = 20 x n

Now, we can write the equation as:

20 x n = 16m + (20n - 16m)

20n - 16m = 4n

n - m = n / 4

m = 3n / 4

So, the mode occurs 3n / 4 times.

Now, we can find the median using the formula.

Median = [(n + 1) / 2]th observation

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Hi friend..
Here is your answer..

If mode = 16
Arithmetic Mean = 20

We know that
Mode = 3 Median - 2 Mean
16 =3 Median - 2(20)
16 = 3 Median - 40
16 + 40 = 3Median
56/3 = Median
Median = 18.6

Hence , We get Median 18.6

Hope this will help you.......