Question

Marks :
1
Q 14: If the difference of mode and median of a data is 24, then the difference
of median and mean is
1. O
12
2. O
24
3. O
00
4.
36

Answer 1

Answer :

If the difference of mode and median of a data is 24, then the difference of median and mean would be 12 . [Option 1 ]

Step-by-step explanation :

Given :

• Difference between mode and median is 24 .

To find :

• We have to calculate the difference of median and mode = ?

SoluTion :

Let us assume that,

• Median = M1

• Mode = M2

As it is given that Difference between mode and median is 24 , So,

M2 - M1 = 24 ⠀⠀⠀⠀eqn(1).

Now,

We know that, Mode of a given data is equal to difference of thrice of median and that of the twice of mode,

❏ M2 = 3 × M1 - 2 × M2⠀⠀⠀eqn(2).

Also,

➟ 3 × M1 = M1 + 2 × M1

➟ M2 = M1 + 2 × M1 - 2 × M2 [Eqn 2]

➟ M2 - M1 = 2 × M1 - 2 × M2

➟ M2 - M1 = 2[ M1 - M2]

➟ M1 - M2 = (M2 - M1) / 2

➟ M1 - M2 = 24/2 = 12 [Eqn 1]

➟ M1 - M2 = 12 or Median - Mode = 12

Some important formulae :

1. The empirical mean median mode relation is given as:

• Mean - Mode = 3 (Mean - Median)

2. If a frequency distribution graph has a symmetrical frequency curve .

• Mean = Median = Mode

3. For Positive Frequency Distribution .

• Mean > Median > Mode

4. For Negative Frequency Distribution .

• Mean < Median < Mode

Answer 2

Answer:

Solution:

Difference of mode and median = 24

So, Mode - Median = 24

-------------------(equation 1)

Now, solve for finding the difference of median and mean.

Mode = 3 Median - 2 Mean

=> Mode - Median = 2 Median - 2 Mean

=> 2(Median - Mean) = Mode - Median = 24

Using equation 1, we get

Median - Mean = 24 / 2

Therefore, Median - Mean = 12

Thus, the difference of median and mean is 12.