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

The median of a data set is 20. If each observation is decreased by 7, what is the median of the new data set?

The sum of 12 observations is 96. If each observation is multiplied by 1.5, what is the sum of the new observations?

The mean of a data set is 8. If 3 is added to each data point, what is the mean of the new data set?

The range of a data set is 30. If each observation is multiplied by -3, what is the range of the transformed data set?

A data set has variance 4. What is the variance of a new data set formed by multiplying each value by 5?

In a distribution, the 90th percentile is 65. After adding 10 to every score, what is the new 90th percentile?

A data set has standard deviation 3. If each data point is divided by 6, find the standard deviation of the resulting data set.

A data set has interquartile range (IQR) equal to 15. After multiplying each observation by 0.4 and then adding 5, find the new IQR.

A data set has mean 50 and standard deviation 5. Convert each data point to a z-score by $z=(x-50)/5$. Find the mean and standard deviation of the z-scores.

A data set has mean 12 and variance 16. Each value is transformed by $y=2x-4$. Find the mean and variance of $y$.

A data set of size $n=8$ has sum of squares $S=200$ and mean $\bar x=3$. Find the variance of the data set formed by adding 2 to each value.

A data set of 10 values has mean 7 and variance 9. Define a new data set by $y_i=4(x_i+2)$. Find the mean and variance of the $y$ data set.