Question Type 5: Given a data set, finding the value of the standard deviation, variance and IQR Bootcamps

Calculate the population standard deviation of the dataset $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Calculate the population variance of the dataset $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Calculate the interquartile range (IQR) of the dataset $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Find the population variance and standard deviation of the dataset $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Determine the effect on the population variance if 5 is added to each data point in $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$ without recalculating from scratch.

Find the population standard deviation and interquartile range (IQR) of the dataset $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

A dataset $y$ is formed by multiplying each element of $x=\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$ by 2. Find the population variance and IQR of $y$.

Calculate the sample standard deviation (using $n-1$ in the denominator) of the dataset $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

Using the interquartile range, identify any outliers in the dataset $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$.

A new data point 10 is added to the dataset $x = \{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$. Calculate the new population variance of the 15-point dataset.

A new dataset $y$ is formed by multiplying each element of $x=\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$ by $-3$. Find the population variance and IQR of $y$.

In the dataset $x=\{2,3,6,7,4,13,19,32,14,23,7,8,12,13\}$, one value was recorded as 19 instead of 9. Recalculate the population variance for the corrected dataset.