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: $\frac{41+38+42+41+45+44+48+35}{8}=41.75$, the median is the mean of the middle items in the sequence $35,38,41, 41, 42, 44, 45, 48$, which is: $(41+42)/2=41.5$, the mode is $41$. 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: $48-35=13$ and the standard deviation is: $\sqrt{\frac{(19-41.75)^2+(23-41.75)^2+...+(34-41.75)^2}{8}}\approx3.7997$ 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 $3$, hence the mean: $41.75\cdot 3=125.25$, the median: $41.5\cdot 3=124.5$, the mode:$41\cdot 3=234$, the range:$13\cdot 3=39$, and the standard deviation: $3.7997\cdot 3=11.3991$.
