The sector graph shows the results of testing a new medication on 1080 patients:
Find the number of patients that showed improvement after using the medication.
Find the number of patients that showed some change after using the medication.
Find the percentage of patients that deteriorated after using the medication.
The number of songs on Maria's iPod are sorted by genre and displayed in the given table:
The data is to be displayed on a sector graph. Find the angle of the sector for each genre.
Construct a sector graph for this data.
| Genre | Number of Songs |
|---|---|
| \text{Rock} | 50 |
| \text{Pop} | 40 |
| \text{Soundtracks} | 20 |
| \text{RnB} | 70 |
The sector graph given represents the market share of four brands:
Given that Brand C is twice as popular as Brand A, find the angle at the centre for Brand D.
The sector graph given represents the number of people taking leave from work at a particular company:
If 25 people took leave in January, how many degrees represents 1 person?
Find the number of people who took leave in November.
Find the number of people who took leave between the beginning of November and the end of March.
Find the percentage who took leave in December. Round your answer to two decimal places.
The divided bar graph shows the percentage of responders in each category when asked what they disliked most about their job:
Find the percentage that disliked the long hours.
If the bar is 23 centimetres long, what length represents "long work hours"? Round your answer to one decimal place.
If 690 people were interviewed in total, how many people responded that they dislike their coworkers?
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?
Find 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?
Consider the following graph:
Do the majority of US voters believe the country is going in the right direction?
What percentage of US voters have an opinion on the direction the country is going in?
What percentage of US voters either disapprove or strongly disapprove of Obama?
Which of the following options is greatest?
The proportion of US voters whom either approve or strongly approve of Obama.
The proportion of US voters whom either strongly approve or strongly disapprove of Obama.
The proportion of US voters whom either disapprove or strongly disapprove of Obama.
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.
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.
The table shows the scores of Student A and Student B in five separate tests:
Find the mean score for Student A.
Find the mean score for Student B.
Find the combined mean of the scores of the two students.
State the highest score overall and the student who obtained that score.
State the lowest score overall and the student who obtained that score.
| Test | Student A | Student B |
|---|---|---|
| 1 | 97 | 78 |
| 2 | 87 | 96 |
| 3 | 94 | 92 |
| 4 | 73 | 72 |
| 5 | 79 | 86 |
For each frequency distribution table, find the median of the scores.
| Score | Frequency |
|---|---|
| 23 | 2 |
| 24 | 26 |
| 25 | 37 |
| 26 | 24 |
| 27 | 25 |
| \text{Score }(x) | \text{Frequency }(f) |
|---|---|
| 10 | 6 |
| 14 | 9 |
| 18 | 6 |
| 21 | 7 |
| 24 | 8 |
The set of marks for a class of students is given below:
92,\, 58,\, 69,\, 58,\, 58,\, 81,\, 58,\, 76,\, 76,\, 76
Organise the data into a frequency table.
Find the total number of students in the class.
Find the number of students who will get a Distinction grade (80 \lt \text{score} \leq 90).
Find the number of students who will get a High Distinction grade (scores above 90).
Find the percentage of students obtaining a High Distinction grade. Round your answer to two decimal places.
A statistician organised a set of data into the frequency table shown:
Complete the frequency distribution table.
Calculate the mean, correct to two decimal places.
Find the range of the scores in the table.
Find the mode of the set of scores in the table.
| \text{Score } (x) | \text{Frequency } (x) | f\times x |
|---|---|---|
| 31 | 12 | |
| 32 | 14 | |
| 33 | 7 | |
| 34 | 20 | |
| 35 | 15 | |
| \text{Totals} |
For a dot plot, describe how we determine the frequency of each score.
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:
In this dot plot, what does each dot represent?
What was the most frequently occurring number of shifts per week?
The goals scored by a football team in their matches are represented in the following dot plot:
Construct a frequency distribution table for this data.
Consider the following the dot plot:
Construct a frequency distribution table for this data.
How many students scored above 20?
How many students scored below 30?
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 total number of points scored from three-point shots during the season?
What was the mean number of points scored each game from 'three-pointers'? Round your answer to two decimal places.
What was the mean number of three point shots per game this 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.
The stem and leaf plot shows the batting scores of two cricket teams, A and B:
State the highest score for Team A.
State 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 stem and leaf plot shows the batting scores of two cricket teams, England and India:
What is the highest score from England?
What is the highest score from India?
Find the mean score of England.
Find the mean score of India.
Calculate the combined mean of the two teams.
| England | India | |
|---|---|---|
| 1\ 0 | 3 | 1\ 2\ 4\ 7 |
| 6\ 6\ 5\ 5\ 5\ 5 | 4 | 0\ 2\ 9 |
| 7\ 3 | 5 | 2\ 5 |
| 6 | 4 |
Key: 1 \vert 2 \vert 4 = 21 \text{ and }24
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 back-to-back stem plots show the number of pieces of paper used over several days by Max’s and Charlie’s students:
Did Max's students use 7 pieces of paper on any day?
Is Charlie's median is higher than Max’s median?
Is the median greater than the mean in both groups?
Which class used more paper?
| Max | 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 |
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
Consider the stem and leaf plot below:
Find the mean, to two decimal places.
Find the mode.
Find the median.
Find the range.
| Leaf | |
|---|---|
| 2 | 4 |
| 3 | 0\ 5\ 5\ 5 |
| 4 | 0\ 2 |
| 5 | 0\ 2\ 9\ 9 |
| 6 | 3\ 3 |
| 7 | 0\ 1 |
| 8 | 0\ 1 |
| 9 | 0\ 0\ 5 |
Key: 2 \vert 4 = 24
Two friends have been growing sunflowers. They have measured the height of their sunflowers to the nearest centimetre, with their results shown below:
-
Tricia: \,39,\, 18,\, 14,\, 44,\, 37,\, 18,\, 23,\, 28
-
Quentin: \,49,\, 25,\, 42,\, 5,\, 47,\, 12,\, 15,\, 8,\, 35,\, 22,\, 28,\, 6,\, 21
Display the data in a back-to-back stem and leaf plot.
Find the median height of Tricia's sunflowers.
Find the median height of Quentin's sunflowers.
Find the mean height of Tricia's sunflowers.
Find the mean height of Quentin's sunflowers. Round your answer to two decimal places.
Which friend generally grows taller plants?
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?
Find the range of pulse rates before exercise.
Find 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
The stem and leaf plot below shows the age of people to enter through the gates of a concert in the first 5 seconds:
Find the median age.
Find the difference between the lowest age and the median.
Find the difference between the highest age and the median.
Find the mean age. Round your answer to two decimal places.
Describe the shape of the data.
| Leaf | |
|---|---|
| 1 | 0\ 1\ 2\ 2\ 3\ 3\ 4\ 4\ 4\ 8\ 8\ 8 |
| 2 | 1\ 7 |
| 3 | 4\ 5\ 5 |
| 4 | 0 |
| 5 | 4 |
Key: 1 | 2 \ = \ 12 years old
When 30 students ran 100 \text{ m}, their times (in seconds) were as follows:
13.5, \quad 15.0, \quad 12.1, \quad 12.5, \quad 17.6, \quad 13.7, \quad 15.7, \quad 18.7, \quad 13.1, \quad 11.8, \\ 12.6, \quad 15.7, \quad 14.4, \quad 15.4, \quad 14.9, \quad 15.0, \quad 18.3, \quad 16.3, \quad 15.4, \quad 15.1, \\ 11.9, \quad 16.1, \quad 14.3, \quad 14.5, \quad 16.3, \quad 14.6, \quad 14.9, \quad 15.0, \quad 16.1, \quad 13.5Construct a stem and leaf plot from the given data.
State if the following are present in the data:
How many students ran the 100 \text{ m} in less than 13.7 seconds?
Find the percentage of students who took more than 14 seconds to run the 100 \text{ m}.
What percentage (correct to one decimal place) of students ran times that were below:
The mean
The median
Describe the shape of the distribution.
Consider the following stem and leaf plots:
Are there any outliers? If so, state the value.
Is there any clustering of data? If so, in what interval?
What is the mode?
Describe the shape of the data, ignoring any outliers present.
| Leaf | |
|---|---|
| 0 | 2 |
| 1 | |
| 2 | |
| 3 | 0\ 3\ 6\ 6 |
| 4 | 1\ 4\ 5\ 6\ 6\ 7 |
| 5 | 0\ 4\ 6\ 7\ 9 |
| 6 | 0 |
Key: 2 \vert 3 = 23
| Leaf | |
|---|---|
| 0 | 5 |
| 1 | 7\ 8 |
| 2 | 0\ 8 |
| 3 | 1\ 3\ 3\ 7\ 8\ 9 |
| 4 | 1\ 3\ 5\ 8\ 8\ 8 |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | 2 |
Key: 2 \vert 3 = 23
Describe the shape of each of the following data sets:
| Leaf | |
|---|---|
| 1 | 6\ 7\ 7 |
| 2 | 2\ 2\ 2\ 2\ 3\ 3\ 3 |
| 3 | 3\ 3\ 3\ 6\ 6\ 6\ 7\ 7\ 7\ 7\ 7 |
| 4 | 4\ 4\ 4\ 4\ 4\ 4 |
| 5 | 7\ 7 |
Key: 2 \vert 3 = 23
| Leaf | |
|---|---|
| 6 | 0\ 2\ 3\ 6\ 7\ 7\ 8 |
| 7 | 3\ 6\ 9 |
| 8 | 0\ 5\ 6\ 7 |
| 9 | 2 |
The reaction time of drivers was tested and recorded in the dot plot below:
Construct a frequency distribution table for the individual data values.
Is the distribution uni-modal, bi-modal, or multi-modal?
State the mode(s).
The line graph shows the amount of petrol (in litres) in a car’s tank during a long drive:
Given that the drive started at 8 am:
How much petrol was initially in the tank?
What happened at 9 am and 1 pm?
How much petrol was used between 1 pm and 5 pm?
To the nearest hour, when did the petrol in the tank first fall below 18 litres?
The graph below shows the median house prices per quarter for the four years to September 2013:
Describe the underlying trend in median house prices over the four years.
State the range of prices over the four year period to the nearest \$100\,000.
List the quarters in which the three highest median house prices occurred.
The table shows the house points earned by four colour houses at their swimming carnival:
Construct a column graph for the data.
| House | \text{Blue} | \text{Green} | \text{Yellow} | \text{Orange} |
|---|---|---|---|---|
| Points | 60 | 20 | 70 | 60 |
The table shows the number of people who visited Disneyland between 2008 and 2012:
| Year | 2008 | 2009 | 2010 | 2011 | 2012 |
|---|---|---|---|---|---|
| Number of people (in hundred thousands) | 158 | 155 | 155 | 157 | 160 |
Construct a column graph for the data.
A survey of the preferred sport was done for a group of boys and the results are shown in the column graph below:
How many boys prefer football to other sports?
Which is the most popular sport?
How many boys took part in the survey?
Construct a frequency table for the histogram shown:
The amount of snowfall (in centimetres) is recorded at the base of the mountain each day:
6, \, 2, \, 0, \, 3, \, 2, \, 2, \, 3, \, 4, \, 2, \, 0, \, 3, \, 2, \, 3, \, 4, \, 6, \, 4, \, 3, \, 0, \, 5, \, 3
Construct a frequency histogram for the data.
On how many days did 3 centimetres of snow fall?
On how many days did at least 4 centimetres of snow fall?
For each of the following graphs:
Find the total number of scores.
Find the median.
Find the range.
State the mode(s).
Consider the following graph:
Find the total number of scores.
Find the sum of the scores.
Find the mean, to two decimal places.
State the mode(s).
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?
From the frequency polygon shown:
Find the number of scores.
Calculate the sum of the scores.
Calculate the mean of the scores, correct to two decimal places.
The frequency polygon shows the frequency of calls made during each day of the week:
How many calls were made on Friday?
What was the maximum number of calls made on a single day?
What was the total number of calls made during the week?
Draw a frequency polygon for the following data sets:
| Score | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Frequency | 8 | 9 | 6 | 3 | 1 |
| Salary | 30\,000 | 40\,000 | 50\,000 | 60\,000 | 70\,000 | 80\,000 |
|---|---|---|---|---|---|---|
| Frequency | 8 | 6 | 7 | 3 | 0 | 1 |
Some people were asked approximately how many of their high school friends they remained in contact with after high school to the nearest 10 friends. The results are presented in the following frequency distribution table:
| Score | 0 | 10 | 20 | 30 | 40 |
|---|---|---|---|---|---|
| Frequency | 5 | 16 | 9 | 8 | 4 |
Construct a frequency histogram for the data.
What was the most common response?
Construct a frequency polygon on top of your histogram.
Using your polygon, estimate the number of people who kept in touch with 35 friends.
State whether the following is true or false:
A frequency polygon only allows you to determine the frequency of each known score.
A frequency polygon allows you to determine the frequency of any score with certainty.
Meteorologists reviewed the rainfall (in \text{mm}) each January over several years at a certain site. The frequency polygon shows the results:
How many years of recordings does the polygon represent?
Find the proportion of years in which there was at least 4\text{ mm} of rainfall in January.
Describe the shape of the data in the following graphs:
