Determine whether the following classify as numerical or categorical data:
Favourite flavours
Minimum temperature
Daily temperature
Types of horses
Amount owing on a purchase
Brands of tablets
Types of folders
Daily UV index
Maximum rainfall
Favorite colours
Brands of phones
Maximum snowfall
Breeds of dogs
Colours of folders
Types of fruits
Car speed
For each of these numerical data types, identify whether they are discrete or continuous:
Number of classrooms at a school
Daily humidity
The ages of a group of people
The time taken to run 200 metres
Lengths of cats' whiskers
The distance from Earth to Mars
How long it takes to fall asleep
Amount paid for walking the dog
The number of people taller than you
The top speed of different motorcycles
The size a coin collection
The amount of soda you drink in a day
The best time for solving a Rubik's cube
The hourly pay rate for a particular job
Number of views of a YouTube channel
The snowfall in your city
Number of children in your sports team
The strength of an earthquake
Amount of money owing on a mortgage
Your marks in a Physics test
State whether the following are nominal or ordinal data:
Eye colour
Your birthdate
Letter grade on a test
Favourite song
State/territory of birth
Year level
Brand of phone
Position in a queue
Classify the following data into the following categories:
- Numerical discrete
- Numerical continuous
- Categorical ordinal
- Categorical nominal
Population of your town
Heights of people at a carnival
Weights of dogs
The languages spoken in your class
For the following surveys, state whether the data found should be grouped or ungrouped when constructing a 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.
Find the class centre for the class interval: 27 - 40.
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.
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 (scores above 90)?
What is the percentage of students obtaining a High Distinction grade? Round your answer to 2 decimal places.
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:
What was the highest price that could have been recorded?
How many days was the price above 140.9 cents?
| 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 | 5 |
| 145.9 - 150.9 | 148.4 | 5 |
The following frequency table below shows the resting heart rate of some people taking part in a study:
Complete the table.
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 |
Sean is working at a fast food restaurant, and decides to take a survey of the age of his customers one evening. The results are shown in the table below:
How many customers did Sean serve that evening?
What percentage of Sean's customers were younger than 20 years old?
What percentage of Sean's customers were 50 or older?
| Age (years) | Frequency |
|---|---|
| a \lt 20 | 8 |
| 20\leq a \lt 35 | 16 |
| 35\leq a \lt 50 | 25 |
| 50\leq a \lt 65 | 21 |
| 65\leq a | 10 |
The time spent by patients waiting at a doctor's office was recorded over one week. The results are shown in the given frequency table.
How many patients visited the doctor this week.
What percentage of patients had to wait half an hour or more?
What percentage of patients were seen within 20 minutes?
| Wait time (mins) | Frequency |
|---|---|
| 0\leq t \lt 10 | 37 |
| 10\leq t \lt 20 | 50 |
| 20\leq t \lt 30 | 24 |
| 30\leq t \lt 40 | 22 |
| 40\leq t \lt 50 | 12 |
| 50\leq t \lt 60 | 2 |
| 60\leq t \lt 70 | 3 |
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 less than 60 \text{ mm} were collected?
What was the most common interval of leaf length collected?
Are leaves more likely to be at least 60 \text{ mm} in length?
Can we conclude from the table that there were no leaves collected with a length less than 5 \text{ mm}. Explain your answer.
| Leaf length, (mm) | 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 \lt 84 | 43 |
The speed of passing cars on a stretch of highway are recorded by a police officer.
The results are shown in the first table:
How many cars did the police officer observe?
The stretch of highway that the police officer was observing had a speed limit of 100\text{ km/h}. How many drivers were recorded to be speeding?
| \text{Speed (km/h)} | \text{Frequency} |
|---|---|
| 80 \lt x\leq 90 | 3 |
| 90 \lt x\leq 100 | 55 |
| 100 \lt x \lt 110 | 10 |
| 110\leq x \lt 120 | 6 |
| 120\leq x \lt 130 | 0 |
| 130\leq x \lt 140 | 1 |
Use the information in the second table, to find:
| Speed over the limit | Fine | Demerit points |
|---|---|---|
| x \lt 10 | 165 | 2 |
| 10\leq x \lt 20 | 350 | 3 |
| 20\leq x \lt 30 | 730 | 5 |
| 30\leq x \lt 45 | 870 | 7 |
Below are the luggage weights of 15 passengers, rounded up to the nearest \text{kg}:
20,\, 21,\, 18,\, 17,\, 19,\, 22,\, 20,\, 17,\, 22,\, 16,\, 21, \,21,\, 18, \,21, \,20
Complete the frequency table.
How many times did someone check-in luggage that weighed more than 19 kilograms?
There is a baggage restriction of 20 kilograms and the airline charges each passenger \$1.50 for every kilogram in their luggage above this restriction.
Find the total amount charged for excess baggage.
| \text{Weight (kg)} | \text{Frequency} |
|---|---|
| 15 \lt x\leq 16 | |
| 16 \lt x\leq 17 | |
| 17 \lt x\leq 18 | |
| 18 \lt x\leq 19 | |
| 19 \lt x \leq 20 | |
| 20 \lt x \leq 21 | |
| 21 \lt x\leq 22 |
The mass of thirty apples, rounded to the nearest gram, from an orchard were measured and recorded below:
Mass (in grams)
86, \quad 91, \quad 96, \quad 100, \quad 105, \quad 110, \quad 116, \quad 102, \quad 106, \quad 111,
119, \quad 87, \quad 94, \quad 98, \quad 102, \quad 106, \quad 113, \quad 93, \quad 96, \quad 103,
106, \quad 114, \quad 108, \quad 99, \quad 104, \quad 109, \quad 95, \quad 103, \quad 101, \quad 104
State the mass of the smallest recorded apple.
State the mass of the largest recorded apple.
Find a suitable class interval width.
Create a frequency table for this set of data.
The mass in grams of fifty laboratory rats are shown below.
391, \quad 401, \quad 379, \quad 419, \quad 382, \quad 433, \quad 412, \quad 321, \quad 359, \quad 407,
400, \quad 415, \quad 365, \quad 344, \quad 424, \quad 461, \quad 429, \quad 399, \quad 406, \quad 347,
423, \quad 364, \quad 413, \quad 393, \quad 391, \quad 383, \quad 388, \quad 436, \quad 394, \quad 452,
385, \quad 406, \quad 354, \quad 397, \quad 447, \quad 384, \quad 332, \quad 376, \quad 370, \quad 318,
351,\quad 432,\quad 391,\quad 436,\quad 379,\quad 418,\quad 369,\quad 446,\quad 345,\quad 416
Select the most suitable class interval width from the following:
5 \text{ g}
20 \text{ g}
50 \text{ g}
100 \text{ g}
Create a frequency table for this set of data.
How many rats are in the most frequent mass category?
How many rats are at least 400\text{ g}?
An online survey asks fifty parents to respond to a range of questions about a school.
The times taken to respond to the survey are shown below (in minutes).
6.5, \quad 8.1, \quad 8.8, \quad 4.6, \quad 5.8, \quad 13.4, \quad 16.2, \quad 20.4, \quad 13.5, \quad 9.1,
8.5, \quad 22.4, \quad 15.8, \quad 17.2, \quad 24.0, \quad 19.8, \quad 5.1, \quad 6.8, \quad 5.1, \quad 13.9,
18.0, \quad 22.5, \quad 7.2, \quad 9.0, \quad 12.8, \quad 16.3, \quad 17.2, \quad 4.2, \quad 5.9, \quad 6.1,
10.0, \quad 5.9, \quad 6.7, \quad 4.3, \quad 15.7, \quad 17.3, \quad 22.1, \quad 24.3, \quad 7.1, \quad 11.3,
12.5, \quad 5.6, \quad 7.6, \quad 10.8, \quad 9.0, \quad 5.6, \quad 21.0, \quad 18.5, \quad 13.1, \quad 8.2
Find a suitable class interval width.
Create a frequency table for this set of data.
What percentage of parents took at least 15 minutes to answer the survey?
What percentage of parents took less than 10 minutes to answer the survey?