Representation of data: Practice Questions

A student records the number of hours spent studying per week for a group of 12 students: 5, 7, 8, 8, 10, 12, 12, 12, 15, 18, 20, 25. Find the median of this data set.

For a set of \(20\) observations of a variable \(x\), the following coded totals are given: \(\sum (x - 10) = 40\) and \(\sum (x - 10)^2 = 580\). Calculate the standard deviation of the data set \(x\).

A set of $$10$$ observations is given as: $$12, 15, 11, 13, 15, 10, 14, 15, 12, 13$$. Find the mode of this data set.

The lower quartile of a data set is \(14.5\) and the upper quartile is \(22.1\). Find the interquartile range (IQR) for this set of data.

A data set consists of the following five values: \(5\), \(8\), \(12\), \(15\), and \(10\). Calculate the mean of this data set.

The median of a set of nine distinct values is \(12\). If the largest value is increased by \(5\), state the new median of the data set.

A distribution is represented by a cumulative frequency graph. The \(10^{\text{th}}\) percentile is \(15\) and the \(90^{\text{th}}\) percentile is \(65\). Calculate the interpental range (the difference between the \(90^{\text{th}}\) and \(10^{\text{th}}\) percentiles).

A data set consists of the values: \(2, 4, 4, 5, 9\). Find the variance of this data set.

A set of raw data consists of the following 8 values: \(12, 15, 18, 12, 20, 15, 22, 12\).
(a) Determine the mode and the median of this data set.
(b) Calculate the mean of these values.

The following table shows the frequency distribution of the ages of 40 members of a sports club:

Age (years): \(20-29\), \(30-39\), \(40-49\), \(50-59\)
Frequency: \(8, 14, 12, 6\)

(a) Calculate an estimate for the mean age of the members.
(b) Identify the modal class for this data set.