Explain when a frequency table is useful to represent a data set.
Mr. Yan asked the students in his class to pick whether they prefer swimming or cycling. He displayed the results in the following frequency table:
How many boys picked swimming?
How many girls picked cycling?
Did more boys prefer swimming or cycling?
| Boys | Girls | |
|---|---|---|
| Swimming | 6 | 11 |
| Cycling | 13 | 15 |
Mr. Westwood asked the students in his class to pick their favourite subject. He displayed the results in the following frequency table:
| Maths | Music | Science | English | |
|---|---|---|---|---|
| Boys | 16 | 8 | 10 | 17 |
| Girls | 11 | 17 | 20 | 19 |
How many students picked Music?
How many girls did not pick Maths as their favourite subject?
Did more boys prefer Music or Science?
Homer rolled two dice. He recorded how many times each die landed on each score in the following frequency table:
How many times did he roll a 1?
How many times did Homer roll Die B?
Did he roll more fours with Die A or Die B?
| Number Rolled | Die A | Die B |
|---|---|---|
| 1 | 16 | 7 |
| 2 | 10 | 20 |
| 3 | 6 | 15 |
| 4 | 5 | 8 |
| 5 | 11 | 6 |
| 6 | 8 | 10 |
Lachlan asked his staff which mode of transport they took to work. The results are displayed in the following frequency table:
How many males caught the train?
How many more females caught the bus than females that caught the train?
How many males did Lachlan survey in total?
| Males | Females | |
|---|---|---|
| Train | 12 | 5 |
| Bus | 20 | 14 |
Lucy tossed three coins. Her results are displayed in the frequency table:
How many times did Lucy toss heads?
How many more times did Coin 1 land on tails than Coin 2?
How many times did Lucy toss the coins in total?
| Heads | Tails | |
|---|---|---|
| Coin 1 | 17 | 16 |
| Coin 2 | 11 | 8 |
| Coin 3 | 15 | 6 |
Monica asked 30 people to choose their favourite type of movie. The results are displayed in the following table:
10 people chose Action, 14 people chose Comedy and 6 people chose Documentary.
What type of movie does each letter represent in the table?
| Type of Movie | Frequency |
|---|---|
| A | 10 |
| B | 14 |
| C | 6 |
Hannah interviewed 29 people about how they get to school. The results are displayed in the following table:
8 go by Bus, 12 go by Car, 9 go by Train, and 13 go by Bicycle.
State which mode of transport belongs in positions A, B, C, and D.
| Transport | Frequency |
|---|---|
| A | 8 |
| B | 12 |
| C | 9 |
| D | 13 |
The average temperature for each month in Tallsville was recorded in the following table:
Which month was the hottest?
Which month was the coldest?
Which two months had the same average temperature?
| Month | Temperature |
|---|---|
| \text{January} | 32 |
| \text{February} | 24 |
| \text{March} | 29 |
| \text{April} | 21 |
| \text{May} | 27 |
| \text{June} | 31 |
| \text{July} | 25 |
| \text{August} | 19 |
| \text{September} | 15 |
| \text{October} | 29 |
| \text{November} | 26 |
| \text{December} | 30 |
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 proportion of trains were on time over the whole week?
| No. of trains on time | No. of late trains | |
|---|---|---|
| Monday | 23 | 28 |
| Tuesday | 12 | 25 |
| Wednesday | 22 | 29 |
| Thursday | 30 | 27 |
| Friday | 11 | 14 |
| Saturday | 15 | 11 |
| Sunday | 14 | 10 |
A gymnast received the following scores over several rounds of back to back competition:
Given that she received these scores over 15 rounds of competition, find the value of A.
State the percentage of rounds for which the gymnast received a score of 8. Round your answer to two decimal places.
State the percentage of rounds the gymnast received a score less than 7. Round your answer to two decimal places.
| Score | Frequency |
|---|---|
| 5 | 4 |
| 6 | 1 |
| 7 | 4 |
| 8 | A |
| 9 | 2 |
Judy rolled a die 29 times. She recorded the frequency of each number rolled in the table shown:
Which number was rolled the most?
Which number did she not roll at all?
| Number rolled | Frequency |
|---|---|
| 1 | 6 |
| 2 | 3 |
| 3 | 0 |
| 4 | 7 |
| 5 | 4 |
| 6 | 9 |
In a survey some people were asked approximately how many minutes they take to decide between brands of a particular product. The results are shown in the frequency table below:
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 |
Mr. Rodriguez recorded the number of pets owned by each of the students in his class. He found that 15 students had no pets, 19 students had one pet, 3 students had two pets and 8 students had three pets.
Create a frequency table showing Mr. Rodriguez's results.
Katrina asked 34 people to choose their favourite fruit. 10 people picked apples, 15 people picked bananas, 6 people picked grapes and 3 people picked pears.
Create a frequency table showing Katrina’s results.
Ben asked 35 people about how many siblings they have. He found that 12 people had no siblings, 15 people had one sibling, 3 people had two siblings and 5 people had three siblings.
Create a frequency table showing Ben's results.
Bob asked 41 of his students to choose their favourite toy. 7 students picked cars, 13 people picked planes, 6 people picked balls and 15 people picked video games.
Create a frequency table showing Bob’s results.
20 people were asked how many hours of sleep they had gotten the previous night. The numbers below are each person’s response:
1, 6, 9, 8, 7, 9, 7, 10, 2, 3, 8, 7, 7, 3, 7, 3, 3, 7, 10, 9
Organise the data into a frequency table.
How many people got 7 hours sleep?
What is the maximum amount of sleep reported by the group?
The set of marks for a class of students is given below:
81, 81, 71, 81, 81, 61, 71, 93, 71, 58, 71, 58, 61, 93, 93, 71, 61, 61, 81, 58, 93
Organise the data into a frequency table.
How many students are there in the class?
How many students will get a Distinction grade (scores above 80 but less than or equal to 90)?
How many students will get a High Distinction grade (scores above 90)?
What is the percentage of students obtaining a High Distinction grade? Round your answer to two decimal places.
Below are the luggage weights of 15 passengers, rounded to the nearest kilogram:
16, 19, 21, 22, 19, 22, 22, 17, 21, 19, 16, 21, 19, 16, 22
Organise the data into a frequency table.
How many times did someone check-in luggage that weighed more than 19 kilograms?
There is a baggage restriction of 20 kilograms. The airline charges each passenger \$1.50 for every kilogram in their luggage above this restriction. How much was charged altogether for excess baggage?
The frequency table below shows the family composition for a number of families:
| Family composition | Frequency | Percentage |
|---|---|---|
| \text{Couple family with no children} | 15 | 37.5 |
| \text{Couple family with children} | 18 | |
| \text{Single parent family} | 6 | |
| \text{Other family} | 1 | 2.5 |
| \text{Total} | 100 |
Complete the frequency table.
How many of these families were single parent families?
How many families were there in total?
Find the percentage of families that were couple families with children.
Find the percentage of families that were couple families without children.
Find the percentage of families that were single parent families.
Given an example of a type of family that could be in the "Other family" category.
40 students were asked which sport they preferred, with possible choices of basketball, soccer and tennis. The responses are summarised in the frequency table below:
| Favourite sport | Frequency | Percentage |
|---|---|---|
| \text{Basketball} | 13 | 32.5 |
| \text{Soccer} | 20 | |
| \text{Tennis} | 17.5 | |
| \text{Total} | 40 | 100 |
Complete the frequency table.
Which was the most popular sport? What percentage of students chose this sport?
Which was the second most popular sport? What percentage of students chose this sport
Which was the least popular sport? What percentage of students chose this sport
The sales of different products are shown in the following horizontal bar graph:
Which is the best-selling product?
How many units of all products were sold in total?
If Product B was sold at \$50 each, find the revenue generated by Product B alone.
Miss Merryweather recorded the hair type and colour of her students in the following graph:
Complete the frequency table:
| Red | Brown | Blonde | Black | |
|---|---|---|---|---|
| Straight | ||||
| Curly |
Robert surveyed a group of people about the type of jobs they had. He recorded the data in the following graph:
Complete the frequency table:
| No Job | Casual | Part time | Full time | |
|---|---|---|---|---|
| Men | ||||
| Women |
A survey was conducted about people's favourite movie genre. The results were plotted in the column graph below:
Complete the frequency table:
| Comedy | Action | Drama | Horror | |
|---|---|---|---|---|
| Women | ||||
| Men |
Mr. Price recorded his students' favourite book genre in the column graph below:
Which book genre is most popular?
Which book genre is least popular?
How many more students prefer Detective books than Drama books?
Miss Yen recorded her students' favourite pets in the column graph below:
Which type of pet is most popular?
Which pet is least popular?
How many students picked a Fish as their favourite pet?
How many students were surveyed in total?
A survey of the preferred sport was done for a group of boys and the results are shown in the bar graph below:
How many boys prefer football to other sports?
Which is the most popular sport?
How many boys took part in the survey?
Mr. Hopkins recorded the hair colours of the students in his class in the column graph below:
Which hair color is most common?
Which hair colour is least common?
How many more students have red hair than students with blonde hair?
Mrs Hubbard recorded her students' favourite fruits in the column graph below.
Which fruit is most popular?
Which fruit is least popular?
How many students chose Pineapples?
What is the total number of students interviewed?
The table shows the number of people who visited Disneyland between 2008 and 2012:
Use the table to create a column graph.
| \text{Year} | \text{Number of people}\\ \text{(hundred thousands)} |
|---|---|
| 2008 | 158 |
| 2009 | 155 |
| 2010 | 155 |
| 2011 | 157 |
| 2012 | 160 |
The table shows the house points earned by four different houses at their swimming carnival:
Use the table to create a column graph.
Which house earned the most points?
Which house earned as many points as the Yellow house and Blue house combined?
| House | Points |
|---|---|
| \text{Yellow} | 15 |
| \text{Blue} | 25 |
| \text{Red} | 40 |
| \text{Green} | 60 |
A survey was conducted asking students from Years 5, 6, 7 and 8 what eye colour they have. The results are shown below using divided bar graphs:
Which grade has the largest percentage of brown-eyed children?
Which grade has the largest percentage of blue-eyed children?
Which grade has the smallest percentage of hazel-eyed children?
Which grade has no green-eyed children?
Which grade has the same percentage of green-eyed children as blue-eyed children?
Georgia's weekly spending is to be represented as a divided bar graph that is 16\text{ cm} long:
If she spends \$880 per week, how much does each centimetre of the divided bar graph represent?
The divided bar graph below shows the popularity of certain types of restaurants in Valentina's home town:
Which type of restaurant is the most popular?
Do more people go to French restaurants or to Thai restaurants?
Which two restaurants are visited by the same number of people?
If 24 people went to an Indian restaurant, approximately how many went to a Mexican restaurant?
The local library constructed divided bar graphs showing the last six months of book loans by category. Assume that the total number of loans was exactly the same for each month.
In which month did subscribers borrow the most business books?
Which month was the best month for children's books?
In which month did people borrow the same number of design books as environment books?
Which book category grew constantly during the 6 months?
During which month did people borrow more fiction books than environmental books?
During which two months did people borrow the same total number of fiction books?
The divided bar graph shows the percentage of responders in each category when asked why they dislike their job:
What percentage dislike the long hours?
If the bar is 23 centimetres long, what length represents "long work hours"? Give your answer to one decimal place.
If 690 people were interviewed in total, how many people dislike their coworkers?
The divided bar graph shows a company’s major expenses:
What percentage of expenses go to marketing?
What percentage of expenses goes to research and production?
A group of people were asked which sport they most watch. The 34\text{ cm} divided bar graph represents their responses, where each centimetre represents 6 people:
If the section for Cricket is 4\text{ cm} long, how many people chose Cricket?
What was the total number of responses?
If the section representing Basketball is 10\text{ cm} long, what is the fraction of people who chose Basketball?
If 34 people chose Tennis, what percentage favour Tennis? Round your answer to two decimal places.
Amongst those surveyed, what was the second most popular sport?
The divided bar graph shows the population of indigenous and non-indigenous children aged between 0 and 4:
What percentage of children aged between 0 and 4 are indigenous?
If the graph is 45 centimetres long in total, how long is the section representing non-indigenous children?
The divided bar graph shows the percentage of total subscriptions that each newspaper has. The Age has 54\,000 subscriptions:
What is 1\% of total subscriptions?
Find the total number of subscriptions.
Use the data from the histogram to complete the following frequency table:
| Score | Frequency |
|---|---|
| 21 | |
| 23 | |
| 25 | |
| 27 | |
| 29 | |
| 31 |
The following histogram shows the average load times for forty two webpages. Use this data to complete the following frequency table:
| Load time (seconds) | Frequency |
|---|---|
| 0\leq \text{time} \lt 3 | |
| 3 \leq \text{time} \lt 6 | 11 |
| 6 \leq \text{time} \lt 9 | |
| 9 \leq \text{time} \lt 12 | 5 |
| 12 \leq \text{time} \lt 15 | 4 |
| 15 \leq \text{time} \lt 18 | |
| 18+ | |
| \text{Total} | 42 |
Consider the following histogram:
Which number occured most frequently?
How many scores of 1 were there?
How many more scores of 1 were there than scores of 4?
The Cancer Council surveyed some random people, asking them to estimate (to the nearest10 hours) approximately how much time they spent in the sun during the previous summer. The frequency histogram shows the results:
How many people were surveyed?
What proportion of responders spent at least 60 hours in the sun?
The following frequency table shows the average time spent travelling to work for fifty people:
| Commute time (minutes) | Frequency |
|---|---|
| 0\leq \text{time} \lt 20 | 14 |
| 20\leq \text{time} \lt 40 | 16 |
| 40 \leq \text{time} \lt60 | 10 |
| 60 \leq \text{time} \lt 80 | 7 |
| 80\leq \text{time} \lt 100 | 3 |
| \text{Total} | 50 |
Construct a histogram to display the data shown in the frequency table.
Determine whether the following statements about the data are accurate:
The data shows that most people travel to work by car or by walking, since most travel times are fairly short, and only a few people travel by bus or train.
The data suggests that people prefer a shorter commute to work. A majority live within 40 minutes travel, and in general the longer the commute the less people there are in that category.
The data suggests that people don't care too much about how far away from work they live. Roughly equal portions of people live less than 40 minutes away and more than 40 minutes away.
The data shows that everyone lives within an hours travel from their work, with the peak amount of people living between 20 and 40 minutes away.
The following frequency table shows the price of the most recent book that seventy two university students bought:
Construct a histogram to display the data shown in the frequency table.
Which groups represent peaks in the data set?
Describe what the data shows regarding the price university stundents generally pay for their books.
| \text{Price }( \$ ) | \text{Frequency} |
|---|---|
| 0-19 | 6 |
| 20-39 | 20 |
| 40-59 | 12 |
| 60-79 | 6 |
| 80-99 | 19 |
| 100-119 | 9 |
| \text{Total} | 72 |
Consider the data shown in the histogram below:
Are there any outliers? If so, state them.
Is there any clustering of data? If so, where does it occur?
What is the mode?
Is the distribution of the data negatively skewed, positively skewed or symmetrical?
Consider the data shown in the histogram below:
Are there any outliers? If so, state them.
What is the mode?
Is the distribution of the data negatively skewed, positively skewed or symmetrical?
The shoe sizes of all the students in a class were measured and the data was presented in a histogram as shown:
Are there any outliers?
Is there any clustering of data? If so, where does it occur?
What is the modal shoe size?
Is the distribution of the data negatively skewed, positively skewed or symmetrical?
Consider the following histogram, representing students' heights in centimetres:
Does the histogram represent grouped data or individual scores?
Which of 155, 135 and 145 is closest to the mean?
Describe the shape of the data in context.
Consider the data shown in the histogram below:
Is the distribution of the data negatively skewed, positively skewed or symmetrical?
What is the approximate mean of this data set?
If a die is rolled for a large number of trials and the number appearing is noted, which histogram would you expect to match the data?
A pair of dice are rolled and the numbers appearing on the uppermost face are added to create a score.
How many combinations would result in a score of:
4
7
10
If a pair of dice are rolled for a large number of trials and the numbers appearing are added to create a score, which histogram would you expect to match the data?
