# Why there is more than one mode in a given distribution?

#1

I am currently studying about the properties of a given distribution and while studying it I faced one distribution in which mode has more than one value which I am not able to understand .

In this plot there is two mode value one at 7 and other at 9.

#2

There can be two clusters in the data, each mode pointing a cluster.

You may want to visualize the histograms by conditioning with the other variables in data set.

#3

Hi @sid100158,

Let’s understand what mode is, mode is simply the highest occuring number in a numeric array.

Now see this array-
1,1,1,2,3,4,5,6,6,6,7,8

As you observe you will notice number 1 & 6 are occuring 3 times each. So this array had two modes 1 & 6.

Hope this helps.

Regards,
Aayush

#4

Hi

you face a mixture of distributions here, you have two normal distributions, one with mu at 7 and the other at 9 (mean, mode). To come back to your point, you have two distributions and not one.
You have a pdf of form F(x) = Sum(wi * fi(x) ), i = 1 & 2 and w is the weight allocated to the single pdf. In your case w1 = w2 = 1 and fi(x) with normal distribution N( 7 or 9, 1.69) ( i have did not calculate the variance , just did approximation).

Hope this help.

Alain

#5

Hi

to complement what I wrote yesterday, go through this document. It gives explanation and yes R code how to calculate the two distributions. Have fun .
Alain

Mixed distribution

#6

In the foot size demonstration given above, the two modes probably represent the Gaussian peaks of overlapping male and female distribution. You can model the frequency of this distribution with a double Gaussian of the form f(x) = a*exp( -(x-x1)^2 / (sqrt(2)sigma1) ) + bexp( -(x-x2)^2 / (sqrt(2)*sigma2) ) and find the parameters using chi-squared minimisation.