2

Let's say I have a data set:- $${1,2,3,4,5}$$

I decide to find the mode though it would not be an appropriate measure of central tendency. But still........

Now this is an exceptional case and for exceptional cases , I have the following rule:-

When the each appears equal number of times or 1 time then all are the mode but sometimes we say that no observation is occurring frequently and hence there is no mode.

This statement looks extremely unclear as they do not describe the case when we do it sometimes.

So I have the following possibilities:-

  1. All are mode

  2. No mode

But the second one looks more accurate as there is no observation occuring frequently yet it is not consistent with the statement.

When the each appears equal number of times or 1 time then all are the mode.

So It's more probable The second one is correct.

But I am not sure what should be correct all mode or no mode as they seem to be in opposition of each other.

Mohd Saad
  • 331
  • 1
    Taking Harald Cramer - Mathematical methods of statistics - 1999, for discrete type $x_n$ is called mode, when $p_n>p_{n-1}$ and $p_n>p_{n+1}$. – zkutch Sep 12 '21 at 09:44
  • 1
    @zkutch I would be grateful if you tell the meaning of the variables. – Mohd Saad Sep 12 '21 at 09:45
  • In mentioned book, on page 168 there is definition of discrete type of distribution, on page 179 definition of mode. Using Cramer's terminology $x_n$ is mass point an $p_n$ corresponding mass. – zkutch Sep 12 '21 at 10:04
  • @,zkutch So, Can I say my second assumption is correct. – Mohd Saad Sep 12 '21 at 10:07
  • 1
    If you are a follower of Harald Cramer and assume, for example, uniform distribution for your case, then - yes. – zkutch Sep 12 '21 at 10:10
  • @zkutch What do you mean by uniform distribution here? – Mohd Saad Sep 12 '21 at 10:41
  • Frequency function is constant. – zkutch Sep 12 '21 at 11:49
  • @zkutch Okay, I follow Harald Cramer so it should be correct. – Mohd Saad Sep 12 '21 at 12:08
  • Definitions of modes of samples differ from one author to another. Almost all agree that 1, 2, 2, 3, 5, 2 has mode 2. Some recognize dual modes, so that 1,1, 5, 3, 2, 5 is bi-modal with modes 1 and 5. Sone would say 1,1,1,2,5,3,5 has mode at 1 and secondary mode at 5 (others wouldn't mention 5). Your definition says 1,2,3,4,5 has five modes, but admits that others would say no mode. // Try to use whatever your text or instructor sets as the convention for your course. – BruceET Sep 12 '21 at 20:49
  • @BruceET I also thought about it but the problem was not the things were correct according to the text. – Mohd Saad Sep 13 '21 at 02:58
  • If you can give a couple of the questions, along with your answers and the answers the text says are correct, then maybe one of use can 'break the code' as the the approved definition on mode. – BruceET Sep 13 '21 at 03:51
  • @BruceET Yes in a similar data set all were the mode in excercise but Why did they say sometimes we say no mode? – Mohd Saad Sep 13 '21 at 06:17

1 Answers1

1

It would seem strange to me to say "The mode of a Poisson distribution with parameter $\lambda$ is $\lfloor \lambda \rfloor$, except when $\lambda$ is a positive integer in which case $\ldots$" and follow this with "$\ldots$ it has no mode."

Instead you might say "$\ldots$ both $\lambda$ and $\lambda-1$ are modes of the distribution" as Wikipedia currently does, or perhaps "$\ldots$ both $\lambda$ and $\lambda-1$ are the values with equal highest probability." In your example, you could say $1,2,3,4,5$ all occur equally often, and more often than any other value. They are in that sense modes of the dataset.

Note that the mode is not really a measure of central tendency. For the exponential distribution, the mode is $0$, the left hand end of its support, and there are other similar examples

Henry
  • 169,616
  • I am not familiar with statistics values like the Greek letter or the exponential distribution so if you can tell it in a bit more basic statistics way, it might be easier. – Mohd Saad Sep 13 '21 at 03:00
  • @MohdSaad - I have added a couple of links that might help give some background on these two distributions – Henry Sep 13 '21 at 09:13
  • Okay, Thank you. I will check if the links help. – Mohd Saad Sep 13 '21 at 10:54