I am working on a project and I am having trouble verifying

I am working on a project and I am having trouble verifying some data. I have a survery for 114 people. 85 answered yes and 29 answered no. I think my mean is 1.34 for yes and 3.93 for no but I am looking for verification. I am also trying to figure out the variance and the standard deviation.

Solution

Are you trying to get the mean and standard deviation of the sample proportion?

If so, then the sample mean proportion is given by

p^ = 85/114 = 0.745614035 [ANSWER, sample mean proportion for yes]

Meanwhile, the sample mean proportion for no is

q^ = 1 - p^ = 0.254385965 [ANSWER, sample mean proportion for no]

Now, for the standard deviation, it is the same for both yes or no:

s(p^) = s(q^) = sqrt(p^ q^ / n) = sqrt(0.745614035*0.254385965/114)

s(p^) = s(q^) = 0.040789763 [ANSWER, sample standard deviation of proportions for yes and no]

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If you meant something else, please resubmit this question indicating what specific mean and standard deviation you would like to have. Thanks!