State whether the following is true about an ordered stem-and-leaf plot:
The scores are ordered.
A stem-and-leaf plot does not give an idea of outliers and clusters.
It is only appropriate for data where scores have high frequencies.
The individual scores can be read on a stem-and-leaf plot.
Construct a stem-and-leaf plot that represents the following data:
24,\, 26,\, 25,\, 37,\, 36,\, 37,\, 37,\, 38,\, 41,\, 46,\, 49,\, 56,\, 67,\, 63,\, 67,\, 68,\, 69,\, 75,\, 80,\, 80
Complete the following frequency table for the data displayed in the adjacent stem-and-leaf plot:
| Score | Frequency |
|---|---|
| 10-19 | |
| 20-29 | |
| 30-39 | |
| 40-49 | |
| 50-59 |
| Leaf | |
|---|---|
| 1 | 1\ 2\ 3\ 7 |
| 2 | 3\ 4\ 7\ 7\ 7\ 9 |
| 3 | 2\ 7\ 9 |
| 4 | 0\ 1\ 1\ 5\ 6 |
| 5 | 2\ 6 |
Key: 1|2=12
The stem-and-leaf plot shows the age of people to enter through the gates of a concert in the first 5 seconds:
How many people passed through the gates in the first 5 seconds?
What was the age of the youngest person?
What was the age of the oldest person?
What proportion of the concert-goers were under 25 years old?
| Leaf | |
|---|---|
| 1 | 2\ 4\ 5\ 6\ 6\ 9\ 9 |
| 2 | 1\ 2\ 6\ 7\ 8\ 9\ 9 |
| 3 | 1\ 3\ 8\ 8 |
| 4 | |
| 5 | 5 |
Key: 1|2= 12 years old
The scores for a recent spelling test are shown in the stem-and-leaf plot. The maximum possible score on the test was 100.
How many students took the test?
What was the highest score on the test?
What test score occurred the most frequently?
How many marks separate the highest score and the most frequent score?
| Leaf | |
|---|---|
| 6 | 2\ 3\ 3\ 6\ 6\ 7 |
| 7 | 0\ 1\ 1\ 1\ 1\ 4\ 5\ 8 |
| 8 | 1\ 1\ 2\ 3\ 4\ 5\ 6\ 9\ 9\ 9 |
| 9 | 4\ 5\ 7\ 9 |
Key: 6|2=62
The level of mercury in 40 fishing waters was tested and recorded. The results are given in the following stem-and-leaf plot:
What was the second highest reading?
In how many places was a reading of 117 or higher recorded?
What was the 11th lowest score?
If the safe level of mercury is recommended to be 109 or lower, what percentage of the places have safe levels of mercury?
| Leaf | |
|---|---|
| 9 | 1\ 3\ 5\ 5\ 6 |
| 10 | 1\ 2\ 4\ 4\ 5\ 5\ 6\ 8\ 9\ 9 |
| 11 | 1\ 1\ 2\ 3\ 3\ 3\ 5\ 6\ 7\ 7\ 7\ 8\ 8\ 8\ 8\ 9 |
| 12 | 2\ 2\ 2\ 2\ 2\ 3\ 4\ 6\ 9 |
Key: 1|2=12 units
A cyclist measured his heart rate immediately after finishing each event in which he competed. The results are recorded in a stem-and-leaf plot, but two values are missing:
He can remember no number appears twice in the plot. What is the smaller missing number?
If both missing numbers sum to 367, what is the second missing number?
Key: 12|3= 123
The size of each earthquake that occurred over a three year period, measured from 0 to 9.9, is recorded in the following stem-and-leaf plot:
What was the size of the largest earthquake measured?
An earthquake of size 6 or greater causes significant damage to buildings. How many of the earthquakes caused significant damage to buildings?
Students are asked to randomly choose an earthquake to report on.
What is the probability that the first person picks an earthquake that measured between 8 and 9 (inclusive)?
| Leaf | |
|---|---|
| 0 | 9 |
| 1 | 1\ 5 |
| 2 | 1\ 2\ 2\ 3\ 3\ 5\ 6\ 6\ 6\ 7\ 9\ 9 |
| 3 | 0\ 2\ 8 |
| 4 | 0\ 6\ 6\ 8\ 8\ 9 |
| 5 | 5\ 7\ 7\ 8 |
| 6 | 0\ 2\ 4\ 4\ 9 |
| 7 | 1\ 5\ 7 |
| 8 | 0\ 4\ 5\ 8 |
Key: 4|6=4.6
The following stem-and-leaf plot shows the results of a survey conducted on the price of concert tickets locally and the price of the same concerts at an international venue:
What was the most expensive ticket price at the international venue?
At the international venue, what percentage of tickets cost between \$90 and \$110 (inclusive)?
At the local venue, what percentage of tickets cost between \$90 and \$100 (inclusive)?
| Local | International | |
|---|---|---|
| 8\ 5\ 5\ 0 | 6 | 3\ 9 |
| 9\ 7\ 6\ 5\ 0 | 7 | 2\ 4\ 7\ 7 |
| 7\ 4\ 1\ 1\ 0 | 8 | 0\ 3\ 4\ 8 |
| 3\ 3\ 3\ 2\ 0 | 9 | 1\ 1\ 1\ 2\ 3 |
| 9 | 10 | 0\ 1\ 1\ 3\ 9 |
Key: 6|1|2 = 16 \text{ and } 12
The stem-and-leaf plot shows the batting scores of two cricket teams, the Grasshoppers and the Cicadas:
What is the highest score for the Grasshoppers?
What is the highest score for the Cicadas?
| Grasshoppers | Cicadas | |
|---|---|---|
| 5\ 0 | 3 | 0\ 3\ 5\ 6\ 8 |
| 8\ 7\ 6\ 4\ 4\ 1 | 4 | 2\ 6 |
| 7\ 3 | 5 | 3\ 5 |
| 6 | 5 |
Key: 6|1|2 = 16 \text{ and } 12
The test scores of 12 students in Music and French are listed below:
Music: \ 79,\, 59,\, 74,\, 94,\, 51,\, 71,\, 93,\, 84,\, 69,\, 61,\, 86,\, 86
French: \ 62,\, 71,\, 64,\, 82,\, 83,\, 99,\, 87,\, 89,\, 66,\, 73,\, 59,\, 76
Display the data as an ordered back-to-back stem-and-leaf plot.
Two friends have been growing sunflowers. They have measured the height of their sunflowers to the nearest centimetre, with their results shown below:
Oliver:\ 15,\, 25,\, 19,\, 15,\, 34,\, 44,\, 38,\, 27
Valentina:\ 7,\, 45,\, 14,\, 22,\, 43,\, 16,\, 21,\, 26,\, 29,\, 49,\, 8,\, 35,\, 2
Display the data as an ordered back-to-back stem-and-leaf plot.
The data below represents how long each student in two different classes could hold their breath for, measured to the nearest second:
Dr Patel's class: 46,\, 34,\, 11,\, 37,\, 64,\, 29,\, 57,\, 17,\, 55,\, 53,\, 63,\, 25,\, 66,\, 49,\, 34
Mr Jones's class: 43,\, 44,\, 67,\, 34,\, 31,\, 23,\, 52,\, 15,\, 18,\, 49,\, 12,\, 55,\, 41,\, 65,\, 26
Display the data as an ordered back-to-back stem-and-leaf plot.
Who is the teacher of the student who can hold their breath the longest?