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

A data set has mean 50 and standard deviation 5. Convert each data point to a z-score by $z=\frac{x-50}{5}$. Find the mean and standard deviation of the z-scores.

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

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?

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 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.

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

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