# Thread: How do I find the mean of categorical data?

1. ## How do I find the mean of categorical data?

here is my problem:

I am doing this lab on streaks in basketball, like 0=miss, 1=hit once, 2= hit two in a row.. so on.

I need to find the mean of this data in terms of its streak, but fathom is not giving me an answer cause my table is all representative, here is my data:

0=40
1=26
2=5
3=6
4=1
5=0
6=0
7=0
8=0
9+=0

For some reason I am just hitting a mental block at trying to find this...
the answer should be between 1 and 2, but I cant see how to do this.

2. wait is it .78?

3. Originally Posted by Warrenx
wait is it .78?
I think you should be thinking mean = expected value for this one. Usually the data is given as exact probabilities, so my terminology may be slightly off since this is just a random sample, but the calculations should be valid.

We take X as the streak length, a discrete random variable, and we assume that the sample distribution reflects the population distribution, so for all intensive purposes the probability of getting a streak of length 0 is

P(0) = 40/78

The expected value is

0*P(0) + 1*P(1) + 2*P(2) + ...

an infinite probability-weighted sum. In this case you should get 58/78 $\approx$ 0.7435897.

That is, we expect over a long period of time that the average streak length will be 58/78.

Increasing sample size should get you closer and closer to the true expected value.

4. Originally Posted by undefined
I think you should be thinking mean = expected value for this one. Usually the data is given as exact probabilities, so my terminology may be slightly off since this is just a random sample, but the calculations should be valid.

We take X as the streak length, a discrete random variable, and we assume that the sample distribution reflects the population distribution, so for all intensive purposes the probability of getting a streak of length 0 is

P(0) = 40/78

The expected value is

0*P(0) + 1*P(1) + 2*P(2) + ...

an infinite probability-weighted sum. In this case you should get 58/78 $\approx$ 0.7435897.

That is, we expect over a long period of time that the average streak length will be 58/78.

Increasing sample size should get you closer and closer to the true expected value.
O that is what I've been doing wrong , sweet thank you very much! Sigh why didn't I see that lol