Question Type 6: Given values of a specific data set and some characteristics, being able to find the similar values for another data set Exercises

The mean of a data set is 10. Find the mean of the data set if each value is tripled.

The mean of a data set is 15. If every observation is increased by 4, what is the new mean?

A data set has mean 12 and variance 9. Each data point is increased by 5. Find the new variance.

A data set has mean 8 and standard deviation 2. If each observation is multiplied by 3, find the new mean and new standard deviation.

For the data set {3,7,7,9,12}, calculate the mean, median, mode, and range. Then determine these measures if each value is increased by 2.

For the data set {4,6,10,14,20}, find the interquartile range (IQR). Then find the IQR if each value is multiplied by 2.

A data set has variance $\sigma^2$. Each data point is transformed by $y=-2x+5$. Express the variance of the new data set in terms of $\sigma^2$.

A data set has mean $\mu=20$, median = 18, mode = 22. If each value is doubled and then 4 is subtracted, find the new mean, median, and mode.

The data set is {5,8,9,12,15}. Find the range and interquartile range (IQR). Then if the highest observation increases by 3 and the lowest decreases by 1, find the new range and IQR.

A data set's lowest value decreases by 2 and the highest increases by 3, while all other values remain unchanged. Describe the effects on the range, interquartile range (IQR), and mean of the data set.

For the data set {2,5,7,11,13,17}, calculate the variance and standard deviation. Then find the variance and standard deviation if each value is multiplied by 4.

Let a data set have mean $\mu$ and standard deviation $\sigma$. If each observation is increased by 10 and then multiplied by 0.5, express the new mean and new standard deviation in terms of $\mu$ and $\sigma$.