22.07 Histograms and pie charts
Construct a histogram to represent the following data sets:
3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8
47, 45, 43, 47, 44, 43, 43, 45, 44, 47, 45, 42, 45, 44, 43, 44, 46, 44, 42, 46, 44, 45, 45, 42
Consider the following histogram:
State the frequency of the score of 43.
Find the total number of scores.
Calculate the sum of the scores.
Calculate the mean, correct to two decimal places.
Complete the frequency table for the data set in the histogram:
| Score | Frequency |
|---|---|
| 22.5 \leq \text{Score} \ <23.5 | |
| 23.5 \leq \text{Score} \ <24.5 | |
| 24.5 \leq \text{Score} \ <25.5 | |
| 25.5 \leq \text{Score} \ <26.5 | |
| 26.5 \leq \text{Score} \ <27.5 | |
| 27.5 \leq \text{Score} \ <28.5 |
A government agency records how long people wait on hold to speak to their representatives. The results are displayed in the given histogram:
| Time on hold in minutes | Frequency |
|---|---|
| 0 \leq \text{Time} \ <1.5 | |
| 1.5 \leq \text{Time} \ <2.5 | |
| 2.5 \leq \text{Time} \ <3.5 | |
| 3.5 \leq \text{Time} \ <4.5 | |
| 4.5 \leq \text{Time} \ <5.5 |
Complete the frequency table based on the data from the histogram.
How many phone calls were made?
How many people were on hold for at least 2.5 minutes?
How many people were on hold for less than 3.5 minutes?
The ages of new mothers in a particular hospital are displayed on the following histogram:
| Age | Frequency |
|---|---|
| 28 \leq \text{Age} \ <30 | |
| 30 \leq \text{Age} \ <32 | |
| 32 \leq \text{Age} \ <34 | |
| 34 \leq \text{Age} \ <36 | |
| 36 \leq \text{Age} \ <38 | |
| 38 \leq \text{Age} \ <40 |
Complete the frequency table based on the histogram.
How many new mothers were there?
How many mothers were under 34 years old?
How many mothers were 36 years old or older?
The Cancer Council conducted a study to determine how long people spend in the sun in a month. They asked 120 participants to wear a detector at all times.
Their results are summarised in the given histogram:
| Hours in Sun | Frequency |
|---|---|
| 0 \leq \text{Hours} \ <10 | |
| 10 \leq \text{Hours} \ <20 | |
| 20 \leq \text{Hours} \ <30 | |
| 30 \leq \text{Hours} \ <40 | |
| 40 \leq \text{Hours} \ <50 | |
| 50 \leq \text{Hours} \ <60 | |
| 60 \leq \text{Hours} \ <70 | |
| 70 \leq \text{Hours} \ <80 | |
| 80 \leq \text{Hours} \ <90 |
Complete the frequency table based on the histogram.
How many participants spent less than 30 hours in the sun? .
What fraction of participants spent at least 60 hours in the sun? .
The given pie chart shows the results of a class survey where students were asked to nominate their favourite food:
Which was the most popular food?
Which two foods were equally popular?
The results of a senatorial election in a European country, where 4000 people voted, are shown in the given pie chart:
Who won the election?
After the election, the winner decides to send promotional packages to everyone they suspect voted for Zorg. How many packages should they prepare?
Every student in year 7 was surveyed on their favourite subject, and the results are displayed in the given pie chart:
Which was the most popular subject?
What percentage of the class selected History, Phys. Ed., or Languages?
If 32 students selected Science, how many students are there in year 7?
The following pie charts show the distribution of nuclear weapons owned by countries around the world:
Which country has the most nuclear weapons according to the pie charts?
Which two countries have around half of the nuclear weapons that are not owned by Russia or the USA?
How many countries have more than 100 nuclear weapons?
A pharmaceutical company runs trials of a potential virus vaccine. There are 1080 volunteers for the trial, and the results are shown in the following table:
| Result | Number of volunteers | Angle size |
|---|---|---|
| \text{Improvement} | 705 | \dfrac{705}{1080}\times 360\degree= 235\degree |
| \text{No change} | 240 | |
| \text{Deterioration} | 135 |
Use your calculator to complete the table and find the angle size for each result.
Hence construct a pie chart to represent this data, labelling each sector piece with the name and angle size.
A business wishes to construct a pie chart to display which month holidays are taken over the summer months. They surveyed 180 employees, and the results are shown in the following table:
| Month | Number of employees | Angle size |
|---|---|---|
| \text{November} | 30 | \dfrac{30}{180}\times 360\degree= 60\degree |
| \text{December} | 40 | |
| \text{January} | 50 | |
| \text{February} | 20 | |
| \text{March} | 40 |
Use your calculator to complete the table and find the angle size for each month.
Hence construct a pie chart to represent this data, labelling each sector piece with the name and angle size.
A marketing company wishes to construct a pie chart to display the market share of smartphone manufacturers. They surveyed 4000 people, and the results are shown in the following table:
| Manufacturer | Responses | Angle size |
|---|---|---|
| \text{Apple} | 2051 | \dfrac{2051}{4000}\times 360\degree= 184.6\degree |
| \text{Samsung} | 967 | |
| \text{Huawei} | 531 | |
| \text{Other} | 451 |
Use your calculator to complete the table and find the angle size for each manufacturer, correct to one decimal place.
Hence construct a pie chart to represent this data.
A teacher surveys 220 students to find their favourite subject and wishes to construct a pie chart to display the data. The survey results are shown in the following table:
| Subject | Number of students | Percentage | Angle size |
|---|---|---|---|
| \text{Maths} | 44 | \dfrac{44}{220}=20\% | 20\% \text{ of} \, 220 = 72\degree |
| \text{English} | 55 | ||
| \text{History} | 33 | ||
| \text{Science} | 77 | ||
| \text{Other} | 11 |
Use your calculator to complete the table and find the percentage of students and angle size for each subject.
Hence construct a pie chart to represent this data, labelling each sector piece with the name and percentage.
The given pie chart was displayed on a news program:
Describe two mathematical errors with this pie chart.
Which of the following images better represents the same information?
