20 people were asked how many hours of sleep they had gotten the previous night. The results are shown below:
1, 6, 9, 8, 7, 9, 7, 10, 2, 3, 8, 7, 7, 3, 7, 3, 3, 7, 10, 9
How many people got 7 hours sleep?
What is the maximum amount of sleep reported by the group?
In a survey, people were asked approximately how many minutes they take to decide between brands of a particular product. The frequency table shows the results:
How many people took part in the survey?
What proportion of people surveyed took 1 minute to make a decision?
| Minutes Taken | Frequency |
|---|---|
| 1 | 13 |
| 2 | 17 |
| 3 | 12 |
Describe the type of data that an ungrouped frequency table is suited to represent.
The following table shows the number of trains arriving either on time or late at a particular station:
How many trains were late on Friday?
How many trains passed through the station on Wednesday?
How many trains were on time throughout the entire week?
What fraction of trains were on time over the whole week?
| Day | Arriving on time | Arriving late |
|---|---|---|
| \text{Monday} | 23 | 38 |
| \text{Tuesday} | 12 | 25 |
| \text{Wednesday} | 22 | 29 |
| \text{Thursday} | 30 | 27 |
| \text{Friday} | 11 | 14 |
| \text{Saturday} | 15 | 11 |
| \text{Sunday} | 14 | 10 |
The set of marks for a class of students is given below:
92, 58, 69, 58, 58, 81, 58, 76, 76, 76
Construct the frequency table for the data.
How many students are there in the class?
How many students will get a Distinction grade (80 \lt \text{Score} \leq 90)?
How many students will get a High Distinction grade (\text{Score} \gt 90)?
What percentage of students obtain a High Distinction grade? Round your answer to 2 decimal places.
A gymnast received the following scores over several rounds of back to back competition:
If she received these scores over 15 rounds of competition, what is the missing value?
In what percentage of rounds did the gymnast receive a score of 8? Round your answer to two decimal places.
In what percentage of rounds did the gymnast score less than 7? Round your answer to two decimal places.
| Score | Frequency |
|---|---|
| 5 | 4 |
| 6 | 1 |
| 7 | 4 |
| 8 | |
| 9 | 2 |
For the following scenarios state whether the data should be represented in a grouped or ungrouped frequency table:
A survey conducted of 1000 people, asking them how many languages they speak
A survey conducted of 1000 people, asking them how many different countries they know the names of
The following frequency table shows the data distribution for the length of leaves collected from a species of tree in the botanical gardens:
How many leaves with lengths less than 40 mm were collected?
How many leaves with lengths less than 60 mm were collected?
Which length interval had the highest frequency?
Based on this data, are leaves most likely to be at least 60 mm in length?
| \text{Length, } x \ \text{(mm)} | \text{Frequency} |
|---|---|
| 0 \leq x \lt 20 | 5 |
| 20 \leq x \lt 40 | 11 |
| 40 \leq x \lt 60 | 19 |
| 60 \leq x \lt 80 | 49 |
| 80 \leq x \leq 84 | 43 |
Construct a grouped frequency table for the following data:
46, 54, 35, 23, 24, 28, 26, 11, 19, 17, 32
83, 68, 39, 42, 86, 66, 64, 76, 63, 43, 65, 83, 63, \\\\ 67, 49, 51, 32, 55, 38, 65, 41, 73, 35, 36, 74
A principal wants to investigate the performance of students at his school studying Engineering. To do this, he has the marks of each student collected into groups and put into a frequency table. Each group of marks is assigned a grade as shown:
Complete the cumulative frequency column.
State the total frequency.
State the class size.
Find the number that approximately three quarters of the scores are greater than.
| \text{Grade} | x | f | cf |
|---|---|---|---|
| E | 0 \leq x < 20 | 7 | |
| D | 20 \leq x < 40 | 16 | |
| C | 40 \leq x < 60 | 35 | |
| B | 60 \leq x < 80 | 102 | |
| A | 80 \leq x < 100 | 72 |
Consider the given frequency table:
Complete the cumulative frequency column.
State the total frequency.
State the class size.
Find the number that approximately one third of the scores recorded are greater than.
| x | f | cf |
|---|---|---|
| 20 \to 24 | 5 | |
| 25 \to 29 | 10 | |
| 30 \to 34 | 15 | |
| 35 \to 39 | 8 | |
| 40 \to 44 | 4 | |
| 45 \to 49 | 2 | |
| 50 \to 54 | 1 |
Consider the given frequency table:
Complete the cumulative frequency column.
State the total frequency.
State the class size.
Find the number such that approximately one third of the scores recorded are greater than to it.
| x | f | cf |
|---|---|---|
| 1 \to 4 | 4 | |
| 5 \to 8 | 5 | |
| 9 \to 12 | 9 | |
| 13 \to 16 | 5 | |
| 17 \to 20 | 4 |
For the given frequency table:
Complete the cumulative frequency column.
Calculate the total frequency.
Identify the class size.
Find the number that approximately half of the scores recorded are greater than.
| x | f | cf |
|---|---|---|
| 1 \to 5 | 16 | |
| 6 \to 10 | 28 | |
| 11 \to 15 | 19 | |
| 16 \to 20 | 17 | |
| 21 \to 25 | 5 | |
| 26 \to 30 | 3 |
If the range of a set of scores is 48, determine the appropriate group size if we wished to group the data into the following number of groups:
3 groups
8 groups
Consider the following set of scores:
30, 67, 24, 51, 49, 53, 36, 24, 57, 66, 26
Determine the set of five class intervals that should be used to analyse this data.
Construct a grouped frequency table for the data.
Consider the following set of scores:
12, 59, 61, 27, 58, 18, 76, 27, 52, 19, 13, 56, 71, 31, 73, \\ 60, 41, 17, 22, 68, 57, 15, 40, 19, 76, 44, 60, 55, 36
Determine the set of seven class intervals that should be used to analyse this data.
Construct a grouped frequency table for the data.
Some data is grouped into class intervals. If one of the class intervals is 5-9, find the upper bound of another class interval with 25 as a lower bound.
Find the class centre of the following class intervals:
The following frequency table shows the resting heart rate of people taking part in a study:
Complete the class centre column.
How many people took part in the study?
How many people had a resting heart rate between 55 and 74?
How many people had a resting heart rate of below 65?
| Heart Rate | Class Centre | Frequency |
|---|---|---|
| 45 - 54 | 15 | |
| 55 - 64 | 25 | |
| 65 - 74 | 26 | |
| 75 - 84 | 30 |
As part of a fuel watch initiative, the price of petrol at a service station was recorded each day for 21 days. The frequency table shows the findings.
| Price (in cents per litre) | Class Centre | Frequency |
|---|---|---|
| 130.9 - 135.9 | 133.4 | 6 |
| 135.9 - 140.9 | 138.4 | 5 |
| 140.9 - 145.9 | 143.4 | 6 |
| 145.9 - 150.9 | 148.4 | 4 |
What was the highest price that could have been recorded?
How many days was the price above 140.9 cents?
If the class centres are taken to be the score in each class interval, find the total of the prices recorded.
Hence, determine an estimate for the average fuel price. Round your answer to two decimal places.
The masses (in \text{kg}) of a group of students are listed below:
59, 64, 61, 60, 66, 57, 57, 61, 67, 60, 65, 64, 59, 57, \\ 67, 60, 64, 60, 55, 55, 65, 55, 64, 61, 65, 61, 58
Complete the following frequency table:
| \text{Class interval (kg)} | \text{Class Centre, }cc | \text{Frequency, }f | f \times cc |
|---|---|---|---|
| 55 - 59 | |||
| 60 - 64 | |||
| 65 - 69 | |||
| \text{Total:} |
State the modal class.
Using the class centres estimate the mean correct to 1 decimal place.
A group of high school students wanted to convince their principal that the school needed air-conditioning. They measured the temperature in a classroom at 1 pm every day during February and recorded the results (in \degree \text{C}) below:
35, 26, 32, 29, 29, 32, 26, 29, 35, 23, 23, 32, 35, 26, \\ 26, 23, 26, 29, 32, 35, 23, 26, 29, 29, 29, 32, 23, 29
Complete the following frequency table:
| \text{Class} | \text{Class Centre, }cc | \text{Frequency, }f | f \times cc |
|---|---|---|---|
| 22 - 24 | |||
| 25 - 27 | |||
| 28 - 30 | |||
| 31 - 33 | |||
| 34 - 36 | |||
| \text{Total:} |
Find the modal class.
Find the average temperature, correct to two decimal places.
A tree farmer measured the height of a newly planted sapling to the nearest centimetre. The results are given below:
16, 17, 27, 36, 16, 27, 22, 37, 17, 17, 26, 22, 37, 27, 22, 21, 26, 27, 37, 31, \\\\27, 37, 27, 21, 22, 32, 32, 36, 17, 32, 31, 37, 27, 26, 37, 32, 36, 27, 26
Find the range.
Construct a grouped frequency table with a class centre column.
Use the class centres to estimate the mean, correct to two decimal places.
In which class interval does the median lie?
Which class is the modal class?
Calculate the percentage of saplings that are at least 25 cm to 1 decimal place.
Calculate the percentage of saplings that have a height lower than 25 cm to 1 decimal place.
The data below represents the life expectancy in various countries:
65, 74, 74, 69, 74, 77, 62, 63, 49, 69, 79, 51, 63, 56, 55, 72, 50, 64, 51, 47
Find the average lifespan amongst these countries.
Construct a grouped frequency table with a class centre column.
Using the class centres, calculate the sum of the scores.
Estimate the average life expectancy amongst these countries.
Find the difference between the two averages calculated in part (a) and part (d).
In product testing, the number of faults detected in producing a certain machinery is recorded each day for several days. The frequency table below shows the results:
Construct a histogram to represent the data.
What is the lowest possible number of faults that could have been recorded on any particular day?
| Number of faults | Frequency |
|---|---|
| 0 - 3 | 10 |
| 4 - 7 | 14 |
| 8 - 11 | 20 |
| 12 - 15 | 16 |
Construct a dot plot that represents the following data:
49, 49, 49, 50, 48, 47, 50, 49, 51, 50, 51, 49, 52, 47, 50, 50, 48, 51, 51, 50, 48, 49, 52, 49, \\\\ 47, 47, 52, 52, 49, 47, 52, 48, 51, 50, 49, 52, 48, 48, 52, 50, 48, 47, 52, 52, 52, 48, 48, 49
The goals scored by a football team in their matches are represented in the following dot plot.
Construct the frequency distribution table for this data.
Consider the following the dot plot:
Construct the frequency distribution table for this data.
How many students scored above 20?
How many students scored below 30?
Sophia is a casual nurse. She used a dot plot to keep track of the number of shifts she did each week for a number of weeks:
What does each dot represent?
What was the most frequently occurring number of shifts per week?
The glass windows for an airplane are cut to a certain thickness, but machine production means there is some variation. The thickness of each pane of glass produced is measured (in millimetres), and the dot plot shows the results:
What is the thinnest pane measured?
What thickness was measured 3 times?
What proportion of windows can be used?
Which thickness can be seen as an outlier?
If the glass is more than 0.1 mm outside the ideal thickness of 11.1 mm, it is not used. How many of the panes measured can be used?
Christa is a casual nurse. She used a dot plot to keep track of the number of shifts she did each week for a number of weeks:
Over how many weeks did Christa record her shifts?
For how many weeks did she work 5 shifts?
How many weeks did she work less than 6 shifts?
If Christa works at least 6 shifts a week, she buys a weekly train ticket. What fraction of the time did she buy a weekly train ticket?
The number of 'three-pointers' scored by a basketball team in each game of the season is represented in the dot plot:
How many games did the team play this season?
In how many games did the team score 2 'three-pointers'?
What was the average number of three pointers per game this season? Round your answer to two decimal places.
The number of 'three-pointers' scored by a basketball team in each game of the season is represented in the dot plot:
What was the total number of points scored from three-pointers during the season?
What was the average number of points scored from three pointers each game of the season? Round your answer to two decimal places.
State whether the following is true or false 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
Consider the stem-and-leaf plot below:
Construct a frequency table for the data.
| 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 scores for a recent spelling test are shown in the stem-and-leaf plot below. 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: 7|6 = 76
The stem-and-leaf plot below 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 level of mercury in 40 fishing waters were tested and recorded. The results are given below:
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? Leave your answer to one decimal place if necessary.
| 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 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 a 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: 1|2 = 12
The data below 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?
What was the median ticket price at the international venue?
What percentage of local ticket prices were cheaper than the international median?
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 | |
|---|---|---|
| 7\ 5\ 2\ 2 | 6 | 0\ 5 |
| 9\ 6\ 5\ 4\ 0 | 7 | 2\ 3\ 8\ 8 |
| 9\ 6\ 5\ 3\ 0 | 8 | 2\ 3\ 7\ 8 |
| 8\ 7\ 4\ 3\ 1 | 9 | 0\ 1\ 6\ 7\ 9 |
| 5 | 10 | 0\ 2\ 3\ 5\ 8 |
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 in an ordered stem-and-leaf plot.
The Stem and Leaf plot shows the batting scores of two cricket teams, A and B:
What is the highest score in Team A?
What is the highest score in Team B?
Find the mean score of Team A.
| A | B | |
|---|---|---|
| 5\ 2 | 3 | 2\ 3\ 5\ 7\ 9 |
| 9\ 8\ 5\ 4\ 2\ 1 | 4 | 2\ 9 |
| 8\ 2 | 5 | 3\ 6 |
| 6 | 4 |
Key: 6 | 1 | 2 = 12 \text{ and } 16
The back-to-back stem and leaf plot shows the number of pieces of paper used over several days by Maximilian’s and Charlie’s students.
What was the least pieces of paper that Maximilian's students used on any given day?
Whose class has the higher median?
Is the median greater than the mean for both classes?
| Maximillian | Charlie | |
|---|---|---|
| 7 | 0 | 7 |
| 3 | 1 | 1\ 2\ 3 |
| 8 | 2 | 8 |
| 4\ 3 | 3 | 2\ 3\ 4 |
| 7\ 6\ 5 | 4 | 9 |
| 3\ 2 | 5 | 2 |
Key: 6 | 1 | 2 = 12 \text{ and } 16
The Stem and Leaf plot shows the test scores of a two Year 7 classes, A and B:
Find the highest score in Class A.
Find the highest score in Class B.
Find the mean score of class A, to two decimal places.
Find the mean score of class B, to two decimal places.
Calculate the overall mean of all of the Year 7 students, rounded to two decimal places.
| Class A | Class B | |
|---|---|---|
| 8\ 3\ 0 | 6 | 2\ 4\ 6 |
| 9\ 7\ 6\ 3\ 1 | 7 | 3\ 5\ 8 |
| 8\ 2 | 8 | 1\ 3\ 6\ 8 |
| 9 | 2\ 5 |
Key: 6 | 1 | 2 = 12 \text{ and } 16
The data below represents how long each student in two different classes could hold their breath for, to the nearest second:
Ms. Smith's class: 56, 36, 15, 64, 47, 45, 65, 55, 15, 29, 32, 23, 50, 67, 37
Mr. Stevens's class: 53, 15, 33, 47, 10, 35, 61, 46, 26, 43, 57, 24, 44, 17, 69
Display the data on a back to back stem-and-leaf plot.
Who teaches the student who can hold their breath the longest?
To determine which class has the stronger breath hold capacity, which measure of average would be most appropriate to use? Explain your answer.
The 10 participants had their pulse measured before and after exercise with results shown in the stem and leaf plot below:
What is the mode pulse rate after exercise?
How many modes are there for the pulse rate before exercise?
What is the range of pulse rates before exercise?
What is the range of pulse rates after exercise?
Calculate the mean pulse rate before exercise.
Calculate the mean pulse rate after exercise.
Explain what affect the exercise has on the pulse rates.
| Before Exercise | After Exercise | |
|---|---|---|
| 5\ 5\ 0 | 5 | |
| 9\ 9\ 7\ 4 | 6 | |
| 4\ 3 | 7 | |
| 0 | 8 | 4 |
| 9 | 5\ 7\ 8 | |
| 10 | 3 | |
| 11 | 3\ 5\ 5 | |
| 12 | 0\ 1 |
Key: 6 | 1 | 2 = 12 \text{ and } 16
Two friends have been growing sunflowers. They have measured the height of their sunflowers to the nearest centimetre, and their results are shown below:
Quentin: 39, 18, 14, 44, 37, 18, 23, 28
Tricia: 49, 25, 42, 5, 47, 12, 15, 8, 35, 22, 28, 6, 21
Display the data on a back to back stem-and-leaf plot.
What is the median length of Tricia's sunflowers?
What is the median length of Quentin's sunflowers?
Who has taller sunflowers overall? Explain your answer.