Averages and Range: Practice Questions

A set of weights (in kg) is recorded as follows: \( 54, 58, 62, 54, 70, 54, 60 \). What is the median weight of this group?

The mean of six numbers is \( 14 \). If a new number \( 28 \) is added to the data set, what is the new mean of the seven numbers?

A set of data consists of the following numbers: \(12, 15, 15, 18, 20, 22, 25\). What is the range of this data set?

A group of 5 students has a mean score of 72. If the scores of four students are 60, 85, 70, and 75, what is the score of the fifth student?

The scores of a student in 5 tests are 78, 82, 85, 90, and 95. What is the mean score?

A student records the scores of five subjects: \( 68, 75, 82, 90, \) and \( 85 \). Calculate the range of these scores.

A dataset consists of four integers: \( 5, 8, 12, \) and \( x \). If the mean of these four numbers is \( 10 \), find the value of \( x \).

The weights of a group of 5 men are  \(68 \text{ kg} \),  \(72 \text{ kg} \),  \(75 \text{ kg} \),  \(80 \text{ kg} \), and  \(w \text{ kg} \).

(a) If the mean weight of the 5 men is  \(74 \text{ kg} \), find the value of  \(w \).
(b) Using the value of  \(w \) from part (a), find the median and the range of the weights of these 5 men.
(c) If a sixth man with a weight of  \(82 \text{ kg} \) joins the group, calculate the new mean weight of the 6 men.