CT3 mode and median

[Bharti Singla]

How to find mode and median of discrete distribution?( Like Binomial, Neg.binomial etc.) I am good in finding mode of continuous dist. by finding maximum value using differentiation and median by integrating and putting it 0.5 .
please rply asap.
Thankyou

 

[Aditya mohan mathur]

Generally for any discrete probability question median and mode can be found out directly by writing the values of probability and their cdf's directly.
Say, mode is the value for which the probability is the maximum and median is that value of x which comes in between.

However, for specific distributions, like binomial distribution we can get mode as:
the value between m-1 and m , where m=(n+1)p. If m itself is an integer, then the distribution has 2 modes , m-1 and m.

For negative binomial distribution type 2, the mode is given by (k-1)q/p
For negative binomial distribution type 1, the mode is given by (k-q)/p

 

[Shikha Agarwal]

So this are specific formula's?

 

[Aditya mohan mathur]

Yes

 

[Shikha Agarwal]

But this aren't mention in ct3 material? So can they be asked in exams(IAI)?

 

[Bharti Singla]

Thankyou
Yes, please tel can they be asked in exam?

 

[Aditya mohan mathur]

Not sure about it.
You can check in the previous papers whether they've been asked.

 

[Bharti Singla]

okk.

 

[Bharti Singla]

one more qus.-
If standard deviation > mean .. then the distribution is not symmetrical, but how do we know whether its positively skewed or negativy skewed?
Plz clarify.

 

[John Lee]

You can't tell...unless we know the range of the values. So there was an IFoA question where the distribution was for claims and so the values must be greater than 0. Then mean was like 100 and the sd like 200. Since we can't go much lower than 100 - most of the spread must be greater than the 100 - hence positively skewed.

 

[Shikha Agarwal]

If we are not provided that our data can take only positive value?
.
Also how to comment if we are given mean and IQR only?

 

[suraj]

one more qus.-
If standard deviation > mean .. then the distribution is not symmetrical, but how do we know whether its positively skewed or negativy skewed?

Not always true. Counterexample - Standard Normal Distribution
SD > Mean but distribution is symmetric.

 

[Bharti Singla]

Then how we can comment on skewness if we have only mean and sd?

 

[suraj]

Then how we can comment on skewness if we have only mean and sd?

You can't. More information is required like range of the values, as John said..

 

[Bharti Singla]

Okk