Exercises: Ordered, back-to-back stem-and-leaf and line plots

The marks of 12 students in a test were: 34, 45, 27, 38, 41, 29, 45, 52, 33, 38, 46, 30.

1. a) Draw an ordered stem-and-leaf diagram with a key.
2. b) State the highest and the lowest mark.
3. c) Find the median.

The number of goals scored by a team in 10 matches was: 2, 0, 1, 3, 2, 2, 1, 0, 4, 2.

1. a) Draw a line plot.
2. b) State the mode.
3. c) Find the range.

Here is an ordered stem-and-leaf diagram, with key $2 \mid 3$ meaning $23$.

1 | 2 5 8

2 | 0 3 3 7

3 | 1 4

1. a) How many values are there?
2. b) Find the mode.
3. c) Find the median.

The times in seconds taken by 15 students to run 100 m were: 14.2, 15.1, 13.8, 16.0, 14.9, 15.5, 13.5, 14.7, 15.8, 16.4, 14.1, 15.0, 13.9, 14.6, 15.3.

1. a) Draw an ordered stem-and-leaf diagram with a key.
2. b) Find the median and the range.
3. c) Find the number of students who took less than 15 seconds.

A line plot shows the number of siblings of 20 students: 0 siblings: 3, 1 sibling: 7, 2 siblings: 5, 3 siblings: 3, 4 siblings: 2.

1. a) Draw the line plot.
2. b) Find the mean number of siblings.
3. c) Find the median and the mode.

The ages of people at two sports clubs, A and B, are:

Club A: 18, 22, 25, 31, 34, 35, 41, 47, 52, 58

Club B: 21, 24, 27, 28, 33, 36, 38, 39, 44, 45

1. a) Draw a back-to-back stem-and-leaf diagram with a key.
2. b) Find the median age of each club.

The scores of 14 students in Maths and in Irish are given.

Maths: 52, 61, 67, 70, 73, 75, 78, 80, 82, 84, 85, 88, 91, 95

Irish: 45, 50, 54, 58, 62, 64, 66, 68, 71, 72, 75, 79, 83, 87

1. a) Draw a back-to-back stem-and-leaf diagram with a key.
2. b) Find the median, range and mean of each subject.
3. c) Compare the distributions and state which subject has the greater spread, justifying your answer.

A stem-and-leaf diagram has key $4 \mid 7$ meaning $4.7$ kg.

3 | 5 8 9

4 | 0 2 2 6 7

5 | 1 3 3 3 8

6 | 4

1. a) Find the mean, median and mode.
2. b) Explain how the diagram shows the shape of the data.
3. c) The value $6.4$ is removed. Find the new mean and median, and say which is affected more.

A teacher says that a line plot is better than a stem-and-leaf diagram for the data set 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7 but a stem-and-leaf is better for 112, 125, 131, 134, 140, 143, 147, 152, 158, 161.

1. a) Draw a suitable display for each set.
2. b) Give a reason for the teacher's choices.
3. c) State the median of each data set.