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: $\frac{62+ 66+ 66+ 68+ 74+ 76+ 78+ 80+ 82}{9}\approx72.44$, the median is the middle item in the sequence $62, 66, 66, 68, 74, 76, 78, 80, 82$, which is: $74$, the mode is $66$. 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: $82-62=20$ and the standard deviation is: $\sqrt{\frac{(62-72.44)^2+(66-72.44)^2+...+(82-72.44)^2}{9}}\approx6.7183$ 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 $1.2$, hence the mean: $72.44\cdot 1.2=86.928$, the median: $74\cdot 1.2=88.8$, the mode:$66\cdot 1.2=79.2$, the range:$20\cdot 1.2=24$, and the standard deviation: $6.7183\cdot 1.2=8.06196$.
