Answer
See below.
Work Step by Step
The mean of $n$ numbers is the sum of the numbers divided by $n$. The median of $n$ is the middle number of the numbers when they are in order (and the mean of the middle $2$ numbers if $n$ is even). The mode of $n$ numbers is the number or numbers that appear(s) most frequently. Hence here the mean: $\frac{15+16+ 17+18+19+21+ 21+ 25}{8}=19$, the median is the mean of the middle items in the sequence $15,16, 17,18,19,21, 21, 25 $, which is: $(18+19)/2=18.5$, the mode is $21$. The range is the difference between the largest and the smallest data value. The standard deviation of $x_1,x_2,...,x_n$ is (where $\overline{x}$ is the mean of the data values): $\sqrt{\frac{(x_1-\overline{x})^2+(x_2-\overline{x})^2+...+(x_n-\overline{x})^2}{n}}$. Hence here the range is: $25-15=10$ and the standard deviation is: $\sqrt{\frac{(15-19)^2+(16-19)^2+...+(25-19)^2}{8}}\approx3.0414$ If we add a constant to every value in a data set then the mean, median, and mode of the new data set can be obtained by adding the constant to the mean, median, and mode of the original data set and the range and standard deviation remain unchanged. Here the constant is $14$. Thus the mean: $19+14=33$, the median: $18.5+14=32.5$, the mode:$21+14=35$, the range:$10$, and the standard deviation: $\approx3.0414$.
