7.07 Tables of data
Miss Merryweather recorded the hair colour and hair type of her students in the following graph:
Complete the following two-way table from the information in the graph:
| Red | Brown | Blonde | Black | |
|---|---|---|---|---|
| Straight | ||||
| Curly |
180 tennis players were asked whether they would support tennis players wearing wireless headsets to receive on court coaching. The results are shown in the table:
Find the missing value in the table.
| Support | Do not support | |
|---|---|---|
| Males | 36 | |
| Females | 76 | 18 |
38 students were asked whether or not they were allergic to nuts and dairy. Data is recorded in the following two-way table:
| Allergic to Nuts | Not Allergic to Nuts | |
|---|---|---|
| Allergic to Dairy | 7 | 6 |
| Not Allergic to Dairy | 10 | 15 |
How many students are allergic to nuts?
How many students are allergic to nuts or dairy, or both?
How many students are allergic to at most one of the two things?
A healthy living initiative asked people to describe how often they go to the gym. The table below summarizes the result:
How many people were surveyed?
If one person is chosen at random, what is the probability that they are a female who frequently attends the gym?
If one person is chosen at random, what is the probability that they attend the gym rarely?
| Male | Female | |
|---|---|---|
| Frequently | 23 | 37 |
| Rarely | 39 | 11 |
A group of tourists were asked whether they spoke Mandarin or Spanish. The result is summarized in the table below:
Complete the table.
How many people speak both languages?
If one person is chosen at random, what is the probability that they speak neither language?
If one person is chosen at random, what is the probability that they speak only one of the languages?
| Spanish | Not Spanish | Total | |
|---|---|---|---|
| Mandarin | 51 | 16 | |
| Not Mandarin | 13 | 20 |
In a study, some people were asked whether they were vegetarian or not. 27 responders said they were vegetarian, of which 8 were children. 18 children said they were not vegetarian, and 21 adults said they are not vegetarians.
Complete the table.
Calculate the proportion of responders that are vegetarian.
Calculate the proportion of adults that are vegetarian.
| Not vegetarian | Vegetarian | |
|---|---|---|
| Children | ||
| Adults |
In a study, some people were asked whether they lie. A partially completed two-way table of the results is shown below:
Complete the table.
Of those in the study, one is chosen at random. Find the probability that they said they never lie.
| Lie | Don't Lie | Total | |
|---|---|---|---|
| Children | 15 | 35 | |
| Adults | 10 | ||
| Total | 60 |
The following table describes the departures of trains out of a train station for the months of March and April:
| Month | Departed on time | Delayed |
|---|---|---|
| \text{March} | 109 | 27 |
| \text{April} | 108 | 50 |
How many trains departed during March and April?
Find the percentage of the trains in April that were delayed, to one decimal place.
Find the percentage of the total number of trains during the two months that were trains that departed on time in March, to one decimal place.
Find the exact probability that a train selected at random in April would have departed on time.
Find the exact probability that a train selected at random from the 2 months was delayed.
A student makes a Venn diagram of students who are late to school, and students who catch the bus to school.
Using the Venn diagram, complete the following table:
| Late | Not late | |
|---|---|---|
| Caught bus | ||
| Didn't catch bus |
60 residents of a city were asked "Do you support the construction of the new train station?". The residents questioned were also classified as living in the North, South or in the inner city.
Using the Venn diagram, complete the following table:
| North | South | Inner | |
|---|---|---|---|
| Yes | |||
| No |
Students in Xanthe's class were asked if they owned a dog and asked if they owned a snake. The following two-way table shows the results of the survey:
| Owns a dog | Doesn't own a dog | |
|---|---|---|
| Owns a snake | 2 | 3 |
| Doesn't own a snake | 13 | 11 |
Construct a Venn diagram that represents the information provided in the two-way table.
A vet has 25 pets visit their practice in a day. The pets are categorised based on whether they have been vaccinated and whether they have been microchipped.
Using the Venn diagram, complete the following table:
| Microchipped | Not Microchipped | |
|---|---|---|
| Vaccinated | ||
| Not vaccinated |
In Australia, 100 random people were surveyed regarding their carbon footprint and where they lived. The people were categorised as living in either an urban or regional location, and as having a high or low carbon emission.
Construct a Venn diagram that represents the information provided in the two-way table.
| Urban | Regional | Total | |
|---|---|---|---|
| High emission | 37 | 13 | 50 |
| Low emission | 24 | 26 | 50 |
| Total | 61 | 39 | 100 |
Vanessa wants to sort a list of 11 numbers based on whether they contain a 3, and whether they are even. The list of terms is shown below:
1, \, 2, \, 3, \, 5, \, 8, \, 13, \, 21, \, 34, \, 55, \, 89, \, 144
If a term from the list is chosen at random, find the probability that it:
Is an even number that doesn't contain a 3.
Contains a 3 or is an odd number.
Is either odd or contains a 3, but not both.
In a particular class, 5 people play both football and tennis, 13 people in total play tennis, and 11 in total play football.
How many people only play football?
How many people play only one sport?
If a random student is chosen from the group, what is the probability that the student only plays tennis?
In a study, a number of people were asked whether they were musicians or not. 29 responders said they were a musician, of which 8 were children. 19 children said they were not musicians, and 12 adults said they are not musicians.
How many people were in the study?
What proportion of responders are musicians?
What proportion of adults are musicians?
A group of 132 students are to choose to study either Mandarin or Spanish (or both). 67 students choose Mandarin and 72 students choose Spanish.
How many students choose both languages?
If a student is picked at random, what is the probability that the student chose Spanish only?
If a student is picked at random, what is the probability that the student has not chosen Mandarin?
A student is making a Venn diagram about politicians in the last two elections. Looking at a group of 24 politicians, 14 ran in the first election and 19 ran in the second election.
Given that every politician examined was in at least one election, how many politicians ran in both elections?
If a politician is randomly chosen in the second election, what is the probability they were also in the first election?
A jeweller has sorted 25 gems based on two categories:
Based on the colour - emerald
Based on the cut - rectangular
If a gem is selected at random, what is the probability that it is:
An emerald or rectangular?
Not emerald or rectangular?
Both emerald and rectangular or neither?
These 25 gems have three different cuts - triangular, rectangular and octagonal. There are three colours of gems - amethysts (purple), emeralds (green) and rubies (red).
How many are triangular or emeralds, but not both?
How many are neither amethysts nor rectangular?
A small magazine asked people from different states to send in a vote on whether they supported Daylight Saving Time, the results are shown in the following figure:
What proportion of people voted "YES"?
What proportion of "NO" votes are from NSW?
Considering just the voters from NSW and ACT, what proportion of the votes are NSW "YES" votes?
In a group of 190 primary and senior students, 88 are primary students. The students fell into three categories of travel to school - by bus, car, or walking. 109 students get to school by bus, of which 52 are primary students. 50 students get to school by car, of which 20 are primary students
How many senior students catch the bus to school?
How many senior students are there in total?
How many senior students walk to school?
The employees of Koala Airlines were discussing where they should hold their end of year party. Of all of the employees:
- 53 would go to a restaurant
- 67 would go to a bowling alley
- 76 would go to a theme park
- 16 would only go to either a restaurant or a bowling alley
- 29 would only go to either a bowling alley or the theme park
- 17 would only go to either a restaurant or the theme park
- 4 would not go to a restaurant or a bowling alley or to the theme park
- 5 would go to all three places
How many people in total work at Koala Airlines?
If the restaurant isn't available, what proportion of the employees still have another option?