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: $\frac{28+31+32+35+35+39+40}{7}\approx34.286$, the median is the middle in the sequence $28, 31, 32, 35, 35, 39, 40$, which is: $35$, the mode is $35$. 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: $40-28=12$ and the standard deviation is: $\sqrt{\frac{(28-34.286)^2+(31-34.286)^2+...+(40-34.286)^2}{7}}\approx 3.9898$
When every value of a data set is multiplied by a constant, the new mean, median, mode, range, and standard deviation can be obtained by multiplying each original value by the constant. Here the constant is $1.5$, hence the mean: $34.286\cdot 1.5=51.429$, the median: $35\cdot 1.5=52.25$, the mode: $35\cdot 1.5=52.25$, the range:$12\cdot 1.5=18$, and the standard deviation: $3.9898\cdot 1.5=5.9847$.
