Question

Which of the following measures of central tendency or variability must (if it exists) be an actual data point.

a) midrange

b)mean

c) mode

d) variance

e) standard

f) deviation

g) median

Answer 1

a) Mid-range is

Thus, it does scaling (divided by 2) and adding of the original observations. Hence, it does not contains the actual point

b) Mean is the average of all the observations. Thus it doesn not may contains the actual point.

c) Mode is the value which is the highest frequency of all the observations. Thus it contains the actual point.

d) Variance is the mean sum of squares of the observations from mean. So it also does not contains the actual point.

e) Standard deviation is root of variance, So it also does not contains the actual point.

f) Median is that value which divides the ordered observations in 2 equal parts. If the number of observations are odd then the median is an actual point but if it is even then it may not be the actual point.