GCSE Maths: Types of data and collecting data (Higher)
Part of the GCSE Maths statistics chapter (Higher). Chapter overview · Foundation version of this lesson · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Types of data and collecting data
Statistics is about collecting facts and numbers (called data), organising them, showing them in charts and graphs, and using them to answer questions. Before we collect anything we must decide what kind of data we have, because the kind of data decides which charts and calculations make sense.
Categorical data is described in words: favourite colour, type of pet, make of car. Numerical data is numbers. Numerical data is either discrete or continuous. Discrete data is counted, so it takes separate values: the number of goals in a match (0, 1, 2, 3 …), shoe sizes, or the number of siblings. You cannot score 2.5 goals. Continuous data is measured, so it can take any value in a range: height, mass, time, temperature. Someone can be 1.6 m, 1.63 m or 1.6342 m tall, depending on how carefully we measure.
Primary data is data that you collect yourself, for example by asking questions or carrying out an experiment. Secondary data is data that someone else has already collected, such as figures from a website, a newspaper or a database. Secondary data is quick to get, but you cannot always be sure how it was collected.
Tally charts and frequency tables. To organise raw data we draw a table. We go through the data one item at a time and make one tally mark for each. Tally marks are drawn in groups of five (four upright lines with one line across them) so they are easy to count. The number of tally marks is the frequency. When there are lots of different numbers, we put the data in classes (groups) such as 10 ≤ x < 20. Classes must not overlap and must leave no gaps, so that every value has exactly one place.
Questionnaires. A questionnaire is a set of questions given to people. A good question is clear and short, is not leading (it must not push people toward one answer, like “Don’t you agree that football is the best sport?”), and has response boxes that cover every answer and do not overlap. For numbers of hours, use boxes like “0 to less than 2”, “2 to less than 4” rather than “0–2” and “2–4”, because 2 would fit in both. A time frame helps (“in a typical week”) and an “Other” or “None” box stops people being forced into a wrong answer.
Two-way tables. A two-way table shows two things at once, such as boys and girls and how they travel to school. Each row adds to its row total, each column adds to its column total, and the totals add to the grand total in the bottom right corner. If one number is missing, find a row or column with exactly one gap and use the total.
Key ideas
- Categorical data is words. Numerical data is numbers: discrete (counted) or continuous (measured).
- Primary data you collect yourself. Secondary data has already been collected by someone else.
- A tally mark is one item. Groups of five are drawn as four upright lines with one across. Frequency = number of tally marks.
- Class intervals must not overlap and must leave no gaps.
- Good questions are clear, not leading, and have response boxes that cover everything without overlapping.
- In a two-way table, rows add to row totals and columns add to column totals.
Key words. Categorical data is described in words. Discrete data is numbers that you count. Continuous data is numbers that you measure.
Method. For each item ask: words or numbers? If numbers, counted or measured?
- (a) Number of text messages. It is a number, and you find it by counting. You cannot send 2.5 messages.Discrete
- (b) Mass of a parcel. It is a number, and you find it by measuring. It could be 1.2 kg, 1.25 kg, 1.253 kg …Continuous
- (c) Favourite film. The answers are names (words), not numbers.Categorical
Check. Ask whether a value halfway between two neighbours makes sense. 2.5 messages does not (discrete). 1.25 kg does (continuous). 2.5 films is not a favourite film name, so it is categorical. ✓
Watch out. A number does not automatically mean continuous. If you count it, it is discrete.
Key words. A frequency table shows how many times each value occurs. The frequency (f) is the number of times. The total of the frequency column is the number of values in the data set.
Method. Go through the list once, putting a tally mark in the right row for every item. Then count the tally marks.
- Make a table with a row for each category. There is one row for each different answer.Football, Netball, Rugby, Tennis
- Go through the data one item at a time, making one tally mark each time. Tally marks are grouped in fives (four upright lines and one across), which makes them easy to count. Tick items off as you go so that none is missed or counted twice.
Sport Tally Frequency Football ||||||| 8 Netball ||||| 6 Rugby ||| 3 Tennis ||| 3 Total 20 - Write the number of tally marks as the frequency. The frequency is how many times each answer occurs.Football: 8, Netball: 6, Rugby: 3, Tennis: 3
- Check the total. The frequencies must add up to the number of items in the list.8 + 6 + 3 + 3 = 20
Check. The list has 20 items and the frequencies total 20. ✓
Watch out. Check that the total frequency equals the number of items. Missing an item or counting one twice is the most common slip.
Key words. Grouped data is data put into classes (groups), such as 10 < x ≤ 20. We lose the exact values, so calculations are estimates. The midpoint of a class is halfway between its two ends.
Method. Put each value in the class it belongs to, making a tally mark each time. Then count the tally marks.
- Look at the inequality signs for each class. The lower end is included in a class like 10 ≤ x < 20, but the upper end is not (it goes in the next class).140 ≤ h < 150 cm
150 ≤ h < 160 cm
160 ≤ h < 170 cm
170 ≤ h < 180 cm - Go through the data, one value at a time, putting a tally mark in its class. Every value belongs to exactly one class. Tick each value off as you go.
Height Tally Frequency 140 ≤ h < 150 cm | 1 150 ≤ h < 160 cm ||||| 6 160 ≤ h < 170 cm ||||| 6 170 ≤ h < 180 cm || 2 Total 15 - Write the number of tally marks as the frequency. 1, 6, 6, 2
- Check the total. The frequencies must add up to the number of values.1 + 6 + 6 + 2 = 15
Check. There are 15 values and the frequencies total 15. ✓
Watch out. A value on the boundary goes in the class whose inequality includes it. Read the < and ≤ signs carefully.
| Travel | Bus | Walk | Car | Total |
|---|---|---|---|---|
| Boys | 14 | ? | 7 | 30 |
| Girls | 11 | 12 | ? | 29 |
| Total | ? | 21 | 13 | 59 |
Method. Find a row or column with only one missing number. Use the fact that rows and columns add to their totals.
- Boys, Walk. The boys’ row total is 30 and the other two cells are 14 and 7.30 − 14 − 7 = 9
- Girls, Car. The girls’ row total is 29 and the other cells are 11 and 12.29 − 11 − 12 = 6
- Total, Bus. The Bus column has 14 boys and 11 girls.14 + 11 = 25
Check. Check the bottom row: 25 + 21 + 13 = 59, which is the grand total. ✓
Watch out. Use the totals given in the table. Subtract the numbers you know from the total of that row or column.
Method. Check the question is clear and that the response boxes cover every answer without overlapping.
- Look for overlap. A student who spends exactly £5 could tick the first or the second box.Overlapping boxes: £5 and £10 are in two boxes each.
- Look for gaps. Someone who spends nothing, or more than £15, has no box.No box for £0 (none) or for more than £15.
- Write an improved question. Add a time frame, remove overlaps, and cover every possibility.“In a typical week, how much do you spend on snacks? None Up to £5 More than £5 up to £10 More than £10”
Check. Test with £5, £0 and £20: each has exactly one box. ✓
Watch out. Response boxes must not overlap and must cover all possible answers.
Watch out
Do not call data continuous just because it is a number. Counted numbers (goals, siblings, shoe sizes, money in pounds and pence) are discrete. Measured quantities (time, height, mass) are continuous.Exercise 24A Types of data and collecting data
Non-calculatorKey words. Categorical data is described in words. Discrete data is numbers that you count. Continuous data is numbers that you measure.
Method. Ask: is the data words or numbers? If it is numbers, is it counted (discrete) or measured (continuous)?
- Ask whether the data is words or numbers. Data in words (colours, brands, types) is categorical. Data in numbers is numerical.The colour of cars in a car park
- If it is numerical, ask: counted or measured? Counted values jump in steps, so they are discrete. Measured values can be any value in a range, so they are continuous.It is a word or label (a category), not a number.
- State the type. Categorical
Check. Test: could you have a value halfway between two neighbouring values (such as 2.5 children)? If not, it is discrete or categorical. ✓
Watch out. Money and shoe sizes look like decimals, but you can only have certain values, so they are discrete. Time, height, mass and length are measured, so they are continuous.
Key words. Categorical data is described in words. Discrete data is numbers that you count. Continuous data is numbers that you measure.
Method. Ask: is the data words or numbers? If it is numbers, is it counted (discrete) or measured (continuous)?
- Ask whether the data is words or numbers. Data in words (colours, brands, types) is categorical. Data in numbers is numerical.The number of goals scored in a football match
- If it is numerical, ask: counted or measured? Counted values jump in steps, so they are discrete. Measured values can be any value in a range, so they are continuous.It is a number, and it is found by counting, so it can only take separate values (such as 0, 1, 2, 3).
- State the type. Discrete
Check. Test: could you have a value halfway between two neighbouring values (such as 2.5 children)? If not, it is discrete or categorical. ✓
Watch out. Money and shoe sizes look like decimals, but you can only have certain values, so they are discrete. Time, height, mass and length are measured, so they are continuous.
Key words. Categorical data is described in words. Discrete data is numbers that you count. Continuous data is numbers that you measure.
Method. Ask: is the data words or numbers? If it is numbers, is it counted (discrete) or measured (continuous)?
- Ask whether the data is words or numbers. Data in words (colours, brands, types) is categorical. Data in numbers is numerical.The time taken to run 100 m
- If it is numerical, ask: counted or measured? Counted values jump in steps, so they are discrete. Measured values can be any value in a range, so they are continuous.It is a number, and it is found by measuring, so it can take any value in a range, including decimals.
- State the type. Continuous
Check. Test: could you have a value halfway between two neighbouring values (such as 2.5 children)? If not, it is discrete or categorical. ✓
Watch out. Money and shoe sizes look like decimals, but you can only have certain values, so they are discrete. Time, height, mass and length are measured, so they are continuous.
Key words. Categorical data is described in words. Discrete data is numbers that you count. Continuous data is numbers that you measure.
Method. Ask: is the data words or numbers? If it is numbers, is it counted (discrete) or measured (continuous)?
- Ask whether the data is words or numbers. Data in words (colours, brands, types) is categorical. Data in numbers is numerical.Shoe size
- If it is numerical, ask: counted or measured? Counted values jump in steps, so they are discrete. Measured values can be any value in a range, so they are continuous.It is a number, and it is found by counting, so it can only take separate values (such as 0, 1, 2, 3).
- State the type. Discrete
Check. Test: could you have a value halfway between two neighbouring values (such as 2.5 children)? If not, it is discrete or categorical. ✓
Watch out. Money and shoe sizes look like decimals, but you can only have certain values, so they are discrete. Time, height, mass and length are measured, so they are continuous.
Key words. Categorical data is described in words. Discrete data is numbers that you count. Continuous data is numbers that you measure.
Method. Ask: is the data words or numbers? If it is numbers, is it counted (discrete) or measured (continuous)?
- Ask whether the data is words or numbers. Data in words (colours, brands, types) is categorical. Data in numbers is numerical.The height of a tree
- If it is numerical, ask: counted or measured? Counted values jump in steps, so they are discrete. Measured values can be any value in a range, so they are continuous.It is a number, and it is found by measuring, so it can take any value in a range, including decimals.
- State the type. Continuous
Check. Test: could you have a value halfway between two neighbouring values (such as 2.5 children)? If not, it is discrete or categorical. ✓
Watch out. Money and shoe sizes look like decimals, but you can only have certain values, so they are discrete. Time, height, mass and length are measured, so they are continuous.
Key words. Categorical data is described in words. Discrete data is numbers that you count. Continuous data is numbers that you measure.
Method. Ask: is the data words or numbers? If it is numbers, is it counted (discrete) or measured (continuous)?
- Ask whether the data is words or numbers. Data in words (colours, brands, types) is categorical. Data in numbers is numerical.A person’s favourite film
- If it is numerical, ask: counted or measured? Counted values jump in steps, so they are discrete. Measured values can be any value in a range, so they are continuous.It is a word or label (a category), not a number.
- State the type. Categorical
Check. Test: could you have a value halfway between two neighbouring values (such as 2.5 children)? If not, it is discrete or categorical. ✓
Watch out. Money and shoe sizes look like decimals, but you can only have certain values, so they are discrete. Time, height, mass and length are measured, so they are continuous.
Method. Primary data is collected by you. Secondary data was already collected by someone else.
- Ask: who collected the data? This tells us whether it is primary or secondary.Sam asked the questions herself.
- Decide. The person using the data collected it themselves.Primary
Check. Primary = “I collected it”; secondary = “somebody else collected it”. ✓
Watch out. Using a database or website for your own project is still secondary data, because someone else collected it.
Method. Primary data is collected by you. Secondary data was already collected by someone else.
- Ask: who collected the data? This tells us whether it is primary or secondary.The Met Office collected the figures; Ali only looked them up.
- Decide. The person using the data did not collect it; it was already collected by someone else.Secondary
Check. Primary = “I collected it”; secondary = “somebody else collected it”. ✓
Watch out. Using a database or website for your own project is still secondary data, because someone else collected it.
Method. Primary data is collected by you. Secondary data was already collected by someone else.
- Ask: who collected the data? This tells us whether it is primary or secondary.The shop collected the sales data itself.
- Decide. The person using the data collected it themselves.Primary
Check. Primary = “I collected it”; secondary = “somebody else collected it”. ✓
Watch out. Using a database or website for your own project is still secondary data, because someone else collected it.
Method. Primary data is collected by you. Secondary data was already collected by someone else.
- Ask: who collected the data? This tells us whether it is primary or secondary.The government collected the figures.
- Decide. The person using the data did not collect it; it was already collected by someone else.Secondary
Check. Primary = “I collected it”; secondary = “somebody else collected it”. ✓
Watch out. Using a database or website for your own project is still secondary data, because someone else collected it.
Key words. A frequency table shows how many times each value occurs. The frequency (f) is the number of times. The total of the frequency column is the number of values in the data set.
Method. Go through the list once, putting a tally mark in the right row for every item. Then count the tally marks.
- Make a table with a row for each category. There is one row for each different answer.Red, Blue, Green, Yellow
- Go through the data one item at a time, making one tally mark each time. Tally marks are grouped in fives (four upright lines and one across), which makes them easy to count. Tick items off as you go so that none is missed or counted twice.
Colour Tally Frequency Red |||| 5 Blue ||||| 6 Green ||| 3 Yellow || 2 Total 16 - Write the number of tally marks as the frequency. The frequency is how many times each answer occurs.Red: 5, Blue: 6, Green: 3, Yellow: 2
- Check the total. The frequencies must add up to the number of items in the list.5 + 6 + 3 + 2 = 16
Check. The list has 16 items and the frequencies total 16. ✓
Watch out. Check that the total frequency equals the number of items. Missing an item or counting one twice is the most common slip.
Key words. A frequency table shows how many times each value occurs. The frequency (f) is the number of times. The total of the frequency column is the number of values in the data set.
Method. Go through the list once, putting a tally mark in the right row for every item. Then count the tally marks.
- Make a table with a row for each category. There is one row for each different answer.0, 1, 2, 3, 4
- Go through the data one item at a time, making one tally mark each time. Tally marks are grouped in fives (four upright lines and one across), which makes them easy to count. Tick items off as you go so that none is missed or counted twice.
Number of siblings Tally Frequency 0 |||| 4 1 ||||||| 8 2 ||||||| 8 3 ||| 3 4 | 1 Total 24 - Write the number of tally marks as the frequency. The frequency is how many times each answer occurs.0: 4, 1: 8, 2: 8, 3: 3, 4: 1
- Check the total. The frequencies must add up to the number of items in the list.4 + 8 + 8 + 3 + 1 = 24
Check. The list has 24 items and the frequencies total 24. ✓
Watch out. Check that the total frequency equals the number of items. Missing an item or counting one twice is the most common slip.
Key words. Grouped data is data put into classes (groups), such as 10 < x ≤ 20. We lose the exact values, so calculations are estimates. The midpoint of a class is halfway between its two ends.
Method. Put each value in the class it belongs to, making a tally mark each time. Then count the tally marks.
- Look at the inequality signs for each class. The lower end is included in a class like 10 ≤ x < 20, but the upper end is not (it goes in the next class).10 ≤ a < 20 years
20 ≤ a < 30 years
30 ≤ a < 40 years
40 ≤ a < 50 years - Go through the data, one value at a time, putting a tally mark in its class. Every value belongs to exactly one class. Tick each value off as you go.
Age Tally Frequency 10 ≤ a < 20 years |||| 5 20 ≤ a < 30 years |||||| 7 30 ≤ a < 40 years |||| 5 40 ≤ a < 50 years ||| 3 Total 20 - Write the number of tally marks as the frequency. 5, 7, 5, 3
- Check the total. The frequencies must add up to the number of values.5 + 7 + 5 + 3 = 20
Check. There are 20 values and the frequencies total 20. ✓
Watch out. A value on the boundary goes in the class whose inequality includes it. Read the < and ≤ signs carefully.
| Travel | Bus | Walk | Car | Total |
|---|---|---|---|---|
| Boys | 14 | ? | 7 | 30 |
| Girls | 11 | 12 | ? | 29 |
| Total | ? | 21 | 13 | 59 |
Method. In a two-way table every row adds up to its row total and every column adds up to its column total. Find a row or column with only one number missing.
- Find the missing number in the boys row, walk column. The row total is 30, and the cells in a row add up to the row total, so subtract the numbers we know.30 − 14 − 7 = 9
- Write the answer. This is the number in the cell the question asks about.9
Check. Add up the completed row and column again: they agree with the totals. ✓
Watch out. Look for a row or column with exactly one missing number first.
Method. In a two-way table every row adds up to its row total and every column adds up to its column total. Find a row or column with only one number missing.
- Find the missing number in the boys row, walk column. The row total is 30, and the cells in a row add up to the row total, so subtract the numbers we know.30 − 14 − 7 = 9
- Find the missing number in the girls row, car column. The row total is 29, and the cells in a row add up to the row total, so subtract the numbers we know.29 − 11 − 12 = 6
- Write the answer. This is the number in the cell the question asks about.6
Check. Add up the completed row and column again: they agree with the totals. ✓
Watch out. Look for a row or column with exactly one missing number first.
Method. In a two-way table every row adds up to its row total and every column adds up to its column total. Find a row or column with only one number missing.
- Find the missing number in the boys row, walk column. The row total is 30, and the cells in a row add up to the row total, so subtract the numbers we know.30 − 14 − 7 = 9
- Find the missing number in the girls row, car column. The row total is 29, and the cells in a row add up to the row total, so subtract the numbers we know.29 − 11 − 12 = 6
- Find the missing number in the total row, bus column. The row total is 59, and the cells in a row add up to the row total, so subtract the numbers we know.59 − 21 − 13 = 25
- Write the answer. This is the number in the cell the question asks about.25
Check. Add up the completed row and column again: they agree with the totals. ✓
Watch out. Look for a row or column with exactly one missing number first.
| Travel | Bus | Walk | Car | Total |
|---|---|---|---|---|
| Boys | 14 | 9 | 7 | 30 |
| Girls | 11 | 12 | 6 | 29 |
| Total | 25 | 21 | 13 | 59 |
Method. Find the Girls row and the Walk column and read where they meet.
- Go to the Girls row. Girls are in the second row.Girls: 11, 12, 6, total 29
- Read the Walk column. Walk is the second column.12 girls walk
Check. 11 + 12 + 6 = 29 girls in total. ✓
Watch out. Read the cell where the row and the column meet.
Method. Students who do not come by car walk or take the bus. Either add those two columns, or take the car total away from the total.
- Find the total who come by car. This is the last column total of cars.7 + 6 = 13
- Take it away from all students. 59 − 13 = 46
Check. Bus + Walk = 25 + 21 = 46. ✓
Watch out. “Not car” means everyone except the car travellers.
Method. Part over whole: the boys who take the bus, over all the boys.
- Find the boys who take the bus. 14
- Write over the number of boys. There are 30 boys.1430
- Simplify. Divide both by 2.1430 = 715
Check. 7 ÷ 15 = 0.467 and 14 ÷ 30 = 0.467. ✓
Watch out. The whole is the number of boys (30), not all 59 students.
| In the choir | Not in the choir | Total | |
|---|---|---|---|
| Girls | 22 | ? | 45 |
| Boys | ? | ? | ? |
| Total | 38 | ? | 80 |
Method. In a two-way table every row adds up to its row total and every column adds up to its column total. Find a row or column with only one number missing.
- Find the missing number in the girls row, not in the choir column. The row total is 45, and the cells in a row add up to the row total, so subtract the numbers we know.45 − 22 = 23
- Write the answer. This is the number in the cell the question asks about.23
Check. Add up the completed row and column again: they agree with the totals. ✓
Watch out. Look for a row or column with exactly one missing number first.
Method. In a two-way table every row adds up to its row total and every column adds up to its column total. Find a row or column with only one number missing.
- Find the missing number in the girls row, not in the choir column. The row total is 45, and the cells in a row add up to the row total, so subtract the numbers we know.45 − 22 = 23
- Find the missing number in the total row, not in the choir column. The row total is 80, and the cells in a row add up to the row total, so subtract the numbers we know.80 − 38 = 42
- Find the missing number in the in the choir column, boys row. The column total is 38, and the cells in a column add up to the column total, so subtract the numbers we know.38 − 22 = 16
- Write the answer. This is the number in the cell the question asks about.16
Check. Add up the completed row and column again: they agree with the totals. ✓
Watch out. Look for a row or column with exactly one missing number first.
Method. In a two-way table every row adds up to its row total and every column adds up to its column total. Find a row or column with only one number missing.
- Find the missing number in the girls row, not in the choir column. The row total is 45, and the cells in a row add up to the row total, so subtract the numbers we know.45 − 22 = 23
- Find the missing number in the total row, not in the choir column. The row total is 80, and the cells in a row add up to the row total, so subtract the numbers we know.80 − 38 = 42
- Find the missing number in the in the choir column, boys row. The column total is 38, and the cells in a column add up to the column total, so subtract the numbers we know.38 − 22 = 16
- Find the missing number in the not in the choir column, boys row. The column total is 42, and the cells in a column add up to the column total, so subtract the numbers we know.42 − 23 = 19
- Write the answer. This is the number in the cell the question asks about.19
Check. Add up the completed row and column again: they agree with the totals. ✓
Watch out. Look for a row or column with exactly one missing number first.
Method. Check whether the question pushes the person towards one answer.
- Look at the wording. “Everyone agrees” and “far too long” suggest that the answer should be yes. This is a leading question and produces biased results.Leading: it pushes people to agree.
- Write a neutral question. Remove the opinion words and offer boxes that cover every answer.“How long does your homework usually take each night? Less than 30 minutes 30 minutes up to 1 hour 1 hour or more”
Check. The new question contains no opinion words and every length of time fits exactly one box. ✓
Watch out. A good question does not hint at the answer wanted.
Method. Test the boxes with different answers.
- Test an answer on a boundary. Someone who watches exactly 5 hours could tick the first or the second box.Overlap at 5 and at 10.
- Test an answer outside the boxes. Someone who watches 20 hours, or none, has no box.Gap: more than 15 hours (and 0 is only just included).
- Say how to fix it. Use boxes like “0 to less than 5”, “5 to less than 10”, “10 to less than 15”, “15 or more”.Non-overlapping boxes that cover every answer.
Check. Try 5, 10, 0 and 20 hours in the new boxes: each fits exactly one box. ✓
Watch out. A single hour such as 5 must belong to exactly one box.
| Pets owned | Frequency |
|---|---|
| 0 | 6 |
| 1 | 9 |
| 2 | 7 |
| 3 | 3 |
| 4 | 2 |
Method. The total of the frequencies is the number of students.
- Add the frequencies. Each frequency is a number of students.6 + 9 + 7 + 3 + 2 = 27
- State the answer. The total frequency is the number of students surveyed.27 students
Check. Count again in a different order. ✓
Watch out. Add the frequencies, not the numbers of pets.
Method. “At least 2” means 2 or more, so add the frequencies for 2, 3 and 4 pets.
- Pick the rows with 2 or more pets. At least 2 includes 2.2 pets: 7, 3 pets: 3, 4 pets: 2
- Add them. 7 + 3 + 2 = 12
Check. Students with fewer than 2 pets: 6 + 9 = 15, and 15 + 12 = 27. ✓
Watch out. “At least 2” includes 2.
Method. Each row is a number of pets multiplied by a number of students.
- Multiply each number of pets by its frequency. 3 students with 2 pets own 6 pets, and so on.0 × 6 = 0
1 × 9 = 9
2 × 7 = 14
3 × 3 = 9
4 × 2 = 8 - Add the results. 0 + 9 + 14 + 9 + 8 = 40
Check. The mean number of pets is 40 ÷ 27 ≈ 1.5, which looks sensible. ✓
Watch out. Multiply the number of pets by the frequency; do not just add the pet numbers.
Method. Decide whether goals are counted or measured.
- Check how goals are found. Goals are counted: 0, 1, 2, 3 …Counted data.
- Apply the definitions. Counted data is discrete. Continuous data is measured and can be any value in a range, such as 2.5.You cannot score 2.5 goals, so the data is discrete.
Check. Can there be a value halfway between 2 and 3 goals? No. ✓
Watch out. Being a number is not enough to be continuous: it must be measured.
Method. Decide who collected the data, and whether the data is counted or measured.
- Who collected it? Sam collected the times herself by asking the students.So the data is primary. Secondary data is data that someone else collected.
- Counted or measured? A travel time is measured and can take any value (such as 12.5 minutes).So the data is continuous.
Check. If Sam had used times from a transport website, the data would be secondary. ✓
Watch out. Writing data down does not make it secondary. What matters is who collected it.
Method. Put the numbers we know into a two-way table, then fill in the rest using totals.
- Set up the table with the known numbers. We know: 50 students in total, 26 boys, 30 who prefer football and 8 girls who prefer football.Totals: Boys 26, Football 30, All 50. Girls prefer football: 8.
- Find the number of girls. Girls are the students who are not boys.50 − 26 = 24 girls
- Find the girls who do not prefer football. Girls that prefer football are 8 of the 24.24 − 8 = 16
- Write that as a fraction of the girls and simplify. Part over whole, and the whole is all 24 girls.1624 = 23
Check. Also: boys who prefer football = 30 − 8 = 22, and boys who do not = 26 − 22 = 4. Row of girls: 8 + 16 = 24. ✓
Watch out. The whole is the number of girls (24), not all 50 students.