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: $\frac{88+91+99+102+102+107}{6}\approx98.167$, the median is the average of the middle $2$ in the sequence $88, 91, 99, 102, 102, 107$, which is: $(99+102)/2=100.5$, the mode is $102$. 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: $107-88=19$ and the standard deviation is: $\sqrt{\frac{(88-98.167)^2+(91-98.167)^2+...+(107-98.167)^2}{6}}\approx 6.6186$
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 $2.5$, hence the mean: $98.167\cdot 2.5=245.4175$, the median: $100.5\cdot 2.5=251.25$, the mode: $102\cdot 2.5=255$, the range:$19\cdot 2.5=47.5$, and the standard deviation: $6.6186\cdot 2.5=16.5465$.
