Question

The ratio of the mode and the median of a set of values is 15:11 find the ratio of their mean and mode

Answer 1

Answer:

Mode = 3 Median - 2 Mean

∴ Mode : Median = 7 : 4

∴ Let, Mode = 7x and Median = 4x

∴7x=3×4x−2 Mean

⇒7x=12x−2 Mean

⇒2Mean=5x⇒Mean=

2

5

x

∴ Mean : Mode =

2

5

x:7x=5x:14x

=5:14

Answer 2

Step-by-step explanation:

Given :-

The ratio of the mode and the median of a set of values is 15:11.

To find :-

Find the ratio of their mean and mode ?

Solution :-

Given that :

The ratio of the mode and the median of a set of values = 15:11

Let they be 15X and 11X

Let the mode = 15X

Let the median = 11X

We know that

The relationship among mean ,median and mode

is Mode = 3 × Median - 2× Mean ----(1)

On Substituting these values in the equation (1)

=> 15X = 3× 11X -2 × Mean

=> 15X = 33X -2 × Mean

=> 15X - 33X = -2 × Mean

=> -18X = -2 × Mean

=> -2× Mean = -18X

=> Mean = -18X/-2

=> Mean = 18X/2

=> Mean = 9X

Now

The ratio of Mean and Mode

=> 9X : 15X

=> 9X/15

=> 9 / 15

=> (3×3)/(3×5)

=> 3/5

=> 3:5

Therefore, Mean : Mode = 3:5

Answer:-

The ratio of Mean and Mode of the set of values is 3:5

Used formulae:-

The relationship among mean, median and mode is given by

Mode = 3 × Median - 2× Mean

• Mode is the most frequent occuring observation of the given data

• Median is the middle term of the data when it is arranged in either ascending order or descending order.

• Mean is the quotient when the sum of all observations is divided by the number of all observations.

• Mean , Median and Mode are Measures of Central Tendency .