The median of a set of observations is always one of the observations. 2. The standard deviation does not change if the same constant is added to…

For an even number of observations the median is the average of the two middle values, which need not be an observation (the median of $1,2,3,4$ is $2.5$). So statement 1 is false. Adding a constant shifts every observation and the mean by the same amount, so the deviations from the mean are unchanged and the standard deviation stays the same. Statement 2 is correct. Spread measures are unaffected by shifts but scale with multiplication.