Question

If the value of mean and median are 40 and 48 find out the most probable value of mode

Answer 1

The most probable value of mode is 64 if value of mean and median are 40 and 48  using empirical relationship Mode = 3 median - 2 mean

Given:

• Value of mean and median are 40 and 48

To Find:

• The most probable value of mode

Solution:

• If distribution is Normal  then Mean = Median = Mode
• When the frequencies are not properly distributed it is called as an asymmetrical / skewed distribution.
• If it is moderately asymmetrical distribution
• the below mentioned empirical relationship holds good
• Mode = 3 median - 2 mean
• it was  given by Karl Pearson

Step 1:

Use empirical formula Mode = 3 median - 2 mean and substitute Mean = 40 and median = 48

Mode = 3(48) - 2(40)

Mode = 144 - 80

Mode = 64

Hence  the most probable value of mode is 64

Answer 2

Given,

Mean = 40

Median = 48

To find,

The value of mode.

Solution,

The value of the mode will be 64.

We can easily solve this problem by following the given steps.

Mode is the number that comes more often in the given observations. For example, for the given observations 2,4,5,6,7, and 6, the mode is 6 because 6 is the number that has been repeated twice.

The formula to find the mode when median and mean is (3×median - 2×mean).

Mode = (3×median - 2×mean)

Mode = (3×48) - (2×40)

Mode = 144 - 80

Mode = 64

Hence, the value of mode is 64.