One-variable data: distributions and measures of center and spread: Practice Questions

A data set consists of the following \( 5 \) numbers: \( 12, 17, 21, 25, \) and \( 30 \). If the number \( 30 \) is replaced with \( 45 \), which of the following statistical measures will increase by the greatest amount?

A data set consists of \( 5 \) positive integers: \( 10, 12, 15, 18 \), and \( x \). If the median of the set is \( 15 \) and the mean is \( 16 \), what is the value of \( x \)?

Two data sets, X and Y, are represented by dot plots. Set X contains the values {20, 21, 22, 23, 24}, and Set Y contains the values {10, 15, 22, 29, 34}. Which of the following statements about the standard deviations of the two sets is true?

A set of data consists of the values {4, 8, 8, 12, 15, 15, 15, 19}. What is the mode of this data set?

The average (mean) weight of \( 10 \) boxes is \( 25 \) kilograms. If two more boxes with weights of \( 30 \) kilograms and \( 38 \) kilograms are added to the group, what is the new average weight, in kilograms, of the \( 12 \) boxes?

A data set consists of 11 positive integers. The values are: 4, 7, 7, 8, 10, 10, 10, 12, 15, 18, and 22. If a new value, 45, is added to the data set, which measure of center or spread—the mean, median, or range—will increase by the greatest amount?

A data set consists of the following 7 numbers: \( 5, 8, 8, 12, 15, 18, 24 \).

Part A: Calculate the mean and the median of the data set.
Part B: If a new number, \( 40 \), is added to the data set, which measure of center (mean or median) will increase by a greater amount? Justify your answer by calculating the new values.