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

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.

For the data set $\{3, 7, 7, 9, 12\}$, calculate the mean, median, mode, and range.

Determine these same measures if each value in the data set is increased by $2$.

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.

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

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 $\sigma$.

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

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

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

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 $\sigma^2$.

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