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: $\frac{58+58+59+62+64+65+67}{7}\approx61.857$, the median is the middle in the sequence $58, 58, 59, 62, 64, 65, 67$, which is: $62$, the mode is $58$. 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: $67-58=9$ and the standard deviation is: $\sqrt{\frac{(58-61.857)^2+(58-61.857)^2+...+(67-61.857)^2}{7}}\approx 3.3564$
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 $4$, hence the mean: $61.857\cdot 4=247.428$, the median: $62\cdot 4=248$, the mode:$58\cdot 4=232$, the range:$9\cdot 4=36$, and the standard deviation: $3.3564\cdot 4=13.4256$.
