Final answer:
The new mean after multiplying each data value by 3 is 96, and the new standard deviation is the square root of the new variance, which is √549. A calculator or software can be used to compute the exact standard deviation value.
Step-by-step explanation:
When every value in a data set is multiplied by a constant, the mean of the data set is also multiplied by that constant. Therefore, if the original mean is 32, then after multiplying each data value by 3, the new mean becomes 32 × 3 = 96.
The standard deviation is the square root of the variance. Since variance is a measure of the squared deviations from the mean, when each data value is multiplied by a constant, the variance is multiplied by the square of that constant. Hence, the new variance is 61 × (3²) = 61 × 9 = 549. The new standard deviation is the square root of this new variance, which is √549.
Using a calculator or computer software, you can find the new standard deviation and round it to the nearest tenth. In practice, to calculate these statistical measures accurately, you might use a graphing calculator or statistical software like SPSS, Excel, or R to compute the standard deviation and other related values.