Stem and Leaf Plots

Show your work for each problem.

1.
In a stem-and-leaf plot the key is $4 \mid 7 = 47$ . Which value does stem 6 with leaf 3 stand for?
1. a)603
2. b)36
3. c)63
4. d)6.3
Answer: 63
With the key $4 \mid 7 = 47$ the stem gives the tens and the leaf the ones, so $6 \mid 3 = 6 \times 10 + 3 = 63$ .
2.
The heights of some plants in cm are shown in this stem-and-leaf plot (key: $2 \mid 3 = 23$ cm):
$\begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array}$
How many plants were measured?
Answer: 11
The rows have 3, 4, 3 and 1 leaves: $3 + 4 + 3 + 1 = 11$ plants.
3.
The value 58 goes into a stem-and-leaf plot with the key $5 \mid 2 = 52$ . What is its leaf?
1. a)5
2. b)0
3. c)58
4. d)8
Answer: 8
58 is split into stem 5 (the tens) and leaf 8 (the ones), written $5 \mid 8$ .
4.
The heights of some plants in cm are shown in this stem-and-leaf plot (key: $2 \mid 3 = 23$ cm):
$\begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array}$
How tall is the shortest plant, in cm?
Answer: 12
The first stem is 1 and its first leaf is 2, so the smallest value is $1 \mid 2 = 12$ cm.
5.
The heights of some plants in cm are shown in this stem-and-leaf plot (key: $2 \mid 3 = 23$ cm):
$\begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array}$
Find the range of the plant heights.
Answer: 30
1. What is the largest value (in cm)? 42
2. What is the smallest value (in cm)? 12
3. What is the range? 30
6.
Make an ordered stem-and-leaf plot of these ages: 34, 27, 41, 29, 36, 22, 38, 45 (key: $2 \mid 2 = 22$ ).
Answer: $2 \mid 2~7~9$ , $3 \mid 4~6~8$ , $4 \mid 1~5$
1. What is the smallest stem? 2
2. What is the largest stem? 4
3. How many leaves go on stem 3? 3
4. What is the last (largest) leaf on stem 2? 9
7.
The heights of some plants in cm are shown in this stem-and-leaf plot (key: $2 \mid 3 = 23$ cm):
$\begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array}$
Find the median plant height.
Answer: 23
1. How many values are there? 11
2. Which position is the median? (n + 1) / 2 = ? 6
3. What is the 6th value (in cm)? 23
8.
The heights of some plants in cm are shown in this stem-and-leaf plot (key: $2 \mid 3 = 23$ cm):
$\begin{array}{r|l} 1 & 2~5~8 \\ 2 & 0~3~3~7 \\ 3 & 1~4~6 \\ 4 & 2 \end{array}$
What is the mode of the plant heights (in cm)?
1. a)23
2. b)31
3. c)27
4. d)20
Answer: 23
Stem 2 has the leaf 3 twice, so 23 cm appears twice. No other value repeats, so the mode is 23.
9.
This stem-and-leaf plot shows how many minutes some people exercised on one day (key: $4 \mid 2 = 42$ minutes):
$\begin{array}{r|l} 3 & 5~8 \\ 4 & 0~2~2~6~9 \\ 5 & 1~3~7 \\ 6 & 0~4 \end{array}$
How many people exercised for 50 minutes or more?
Answer: 5
Stem 5 has 3 leaves (51, 53, 57) and stem 6 has 2 (60, 64): $3 + 2 = 5$ people.
10.
This stem-and-leaf plot shows how many minutes some people exercised on one day (key: $4 \mid 2 = 42$ minutes):
$\begin{array}{r|l} 3 & 5~8 \\ 4 & 0~2~2~6~9 \\ 5 & 1~3~7 \\ 6 & 0~4 \end{array}$
Find the median number of minutes.
Answer: 47.5
1. How many values are there? 12
2. With 12 values the median lies between the 6th and 7th values. What is the 6th value? 46
3. What is the 7th value? 49
4. What is the median? 47.5
11.
How are the values 7, 12 and 15 written in a stem-and-leaf plot with the key $1 \mid 2 = 12$ ?
1. a) $7 \mid 0$ and $1 \mid 2~5$
2. b) $0 \mid 7~1~2~5$
3. c) $1 \mid 7~2~5$
4. d) $0 \mid 7$ and $1 \mid 2~5$
Answer: $0 \mid 7$ and $1 \mid 2~5$
7 has 0 tens and 7 ones, so it is $0 \mid 7$ . 12 and 15 share the stem 1 with leaves 2 and 5: $1 \mid 2~5$ .
12.
The 100 m times of 8 runners in seconds are shown here (key: $13 \mid 5 = 13.5$ seconds):
$\begin{array}{r|l} 12 & 4~8 \\ 13 & 1~1~5~9 \\ 14 & 2~6 \end{array}$
What is the range of the times, in seconds? Give a decimal number.
Answer: 2.2
Largest $14 \mid 6 = 14.6$ s, smallest $12 \mid 4 = 12.4$ s, range $14.6 - 12.4 = 2.2$ seconds.
13.
Five friends recorded how many push-ups they could do (key: $2 \mid 4 = 24$ ):
$\begin{array}{r|l} 2 & 4~6 \\ 3 & 0~5~5 \end{array}$
Find the mean number of push-ups.
Answer: 30
1. What is the sum of all values? 150
2. How many values are there? 5
3. What is the mean? 30
14.
The 100 m times of 8 runners in seconds are shown here (key: $13 \mid 5 = 13.5$ seconds):
$\begin{array}{r|l} 12 & 4~8 \\ 13 & 1~1~5~9 \\ 14 & 2~6 \end{array}$
Find the median time.
Answer: 13.3
1. How many times are there? 8
2. What is the 4th time (in seconds)? 13.1
3. What is the 5th time (in seconds)? 13.5
4. What is the median (in seconds)? 13.3
15.
This back-to-back plot shows the points two basketball teams scored per game (key: $2 \mid 1 = 12$ for Team A, $1 \mid 5 = 15$ for Team B):
$\begin{array}{r|c|l} \text{Team A} & \text{Stem} & \text{Team B} \\ \hline 7~2 & 1 & 5 \\ 8~5~4~1 & 2 & 0~3~6 \\ 3~0 & 3 & 1~4~4~8 \\ & 4 & 2~5 \end{array}$
By how many points is Team B's median higher than Team A's?
Answer: 8
1. How many games did Team A play? 8
2. Team A in order is 12, 17, 21, 24, 25, 28, 30, 33. What is its median? 24.5
3. Team B in order is 15, 20, 23, 26, 31, 34, 34, 38, 42, 45. What is its median? 32.5
4. What is the difference of the medians? 8
16.
This back-to-back plot shows the points two basketball teams scored per game (key: $2 \mid 1 = 12$ for Team A, $1 \mid 5 = 15$ for Team B):
$\begin{array}{r|c|l} \text{Team A} & \text{Stem} & \text{Team B} \\ \hline 7~2 & 1 & 5 \\ 8~5~4~1 & 2 & 0~3~6 \\ 3~0 & 3 & 1~4~4~8 \\ & 4 & 2~5 \end{array}$
Which team's points have the larger range?
1. a)Both teams, range 21
2. b)Team A, range 21
3. c)Team A, range 33
4. d)Team B, range 30
Answer: Team B, range 30
Team A: $33 - 12 = 21$ . Team B: $45 - 15 = 30$ . Team B has the larger range. (33 is Team A's largest value, not its range.)
17.
This back-to-back plot shows the points two basketball teams scored per game (key: $2 \mid 1 = 12$ for Team A, $1 \mid 5 = 15$ for Team B):
$\begin{array}{r|c|l} \text{Team A} & \text{Stem} & \text{Team B} \\ \hline 7~2 & 1 & 5 \\ 8~5~4~1 & 2 & 0~3~6 \\ 3~0 & 3 & 1~4~4~8 \\ & 4 & 2~5 \end{array}$
In how many games did Team B score more than 30 points?
Answer: 6
Team B scored 31, 34, 34, 38 (stem 3) and 42, 45 (stem 4): $4 + 2 = 6$ games.
18.
The scores of 11 players in a video game level are 41, 42, 44, 46, 47, 47, 48, 52, 53, 55, 58. They are shown with split stems: the first row of each stem holds the leaves 0-4, the second row the leaves 5-9 (key: $4 \mid 1 = 41$ ).
$\begin{array}{r|l} 4 & 1~2~4 \\ 4 & 6~7~7~8 \\ 5 & 2~3 \\ 5 & 5~8 \end{array}$
Answer the questions about the plot.
Answer: 47
1. How many leaves are in the first row of stem 4 (leaves 0-4)? 3
2. How many leaves are in the second row of stem 4 (leaves 5-9)? 4
3. How many leaves are there in total? 11
4. What is the median? (It is the 6th value.) 47