Measures of dispersion: Practice Questions

A set of data has an interquartile range (IQR) of \(15\). If every item in the set is multiplied by \(4\), what is the new interquartile range of the data set?

The mean and the variance of a set of data \(\{x_1, x_2, \dots, x_n\}\) are \(m\) and \(v\) respectively. A new set of data \(\{y_1, y_2, \dots, y_n\}\) is created such that \(y_i = 5 - 3x_i\) for \(i = 1, 2, \dots, n\). Which of the following gives the mean and the variance of the new set of data?

In a public examination, the scores follow a normal distribution. Alice's score is 72 and her standard score is 0.8. Bob's score is 54 and his standard score is -0.4. If Charlie's score is at the 84.13th percentile of the distribution, find Charlie's score.
(Given: For a standard normal variable \(Z\), \(P(Z < 1) \approx 0.8413\).)</p>

A set of five distinct positive integers, S, is given by \(S = \{x_1, x_2, 8, 12, 16\}\), where \(x_1 \) and \(x_2 \) are integers such that \(x_1 < x_2\). The mean of the data set S is 10, and its standard deviation is \(\sqrt{12.8}\).
Find the interquartile range (IQR) of the set S.

Data Set A consists of 10 numbers and has a mean of 50 and a standard deviation of 4. Data Set B consists of 15 numbers and has a mean of 60. If Data Set A and Data Set B are combined to form Data Set C, the standard deviation of Data Set C is \(\sqrt{33}\). Find the variance of Data Set B.

A set of data \(X\) has a variance of \(9\). A new set of data \(Y\) is obtained from \(X\) by the transformation \(Y = 4 - 2X\). Calculate the standard deviation of the new set of data \(Y\).

The number of hours spent on exercise by 7 students in a week is recorded as follows:
\(2, 5, 5, 8, 10, 12, 15\)

(a) Find the range of the data.

(b) Find the inter-quartile range of the data.

(c) If each student increases their exercise time by 3 hours, find the new range and the new inter-quartile range of the dataset.