Question

Is the sample mean always the most frequently occurring value? If so, explain why. If not, give an example.

Answer 1

Answer:

No the sample mean is not the most frequently occurring data.

Explanation:

If we take a number of observation in an experiment the most frequently repeating value is known as mode of data.

Mean of data is the the value to which all the given observational values are closest.

Consider a given set of observations as

1,1,1,1,1,5,4,3,4

The Mean of the above data set is$\bar{x}=\frac{1+1+1+1+1+1+5+4+3+4}{10}=2$ While as the most often repeating value is 1 which is not equal to mean