Hard GCSE Charts and tables Questions

Read the scale on the vertical axis

Before reading anything off a chart, check what one square on the frequency axis is worth. Here the numbered ticks go up in equal steps, so the height of a bar is read straight off the axis.

Read the bar for Monday

The top of the Monday bar lines up with $5$ on the frequency axis, so there are $5$ cakes for Monday.

Read the bar for Tuesday

The top of the Tuesday bar lines up with $11$ on the frequency axis, so there are $11$ cakes for Tuesday.

Read the bar for Wednesday

The top of the Wednesday bar lines up with $14$ on the frequency axis, so there are $14$ cakes for Wednesday.

Read the bar for Thursday

The top of the Thursday bar lines up with $9$ on the frequency axis, so there are $9$ cakes for Thursday.

Read the bar for Friday

The top of the Friday bar lines up with $5$ on the frequency axis, so there are $5$ cakes for Friday.

Work out the total

Several of the statements talk about the total, so add all the frequencies: there are $44$ cakes altogether.

Note the biggest and the smallest bar

Statements about "the most" and "the fewest" can be settled straight away: the tallest bar is Wednesday and the shortest is Monday.

Test the statement "Thursday has 4 more cakes than Monday."

Check it against the data ($\text{Monday} = 5, \text{Thursday} = 9$). It is true, so this is the correct statement.

Test the statement "Thursday has twice as many cakes as Monday."

Check it against the data ($\text{Monday} = 5, \text{Thursday} = 9$). It does not match the data, so this statement is wrong.

Test the statement "Monday has the fewest cakes."

Check it against the data ($\text{Monday} = 5$). It does not match the data, so this statement is wrong.

Test the statement "The total number of cakes is 41."

Check it against the data (total = 44). It does not match the data, so this statement is wrong.

Test the statement "Wednesday and Friday have the same number of cakes."

Check it against the data ($\text{Wednesday} = 14, \text{Friday} = 5$). It does not match the data, so this statement is wrong.

Count how many statements are true

Exactly one of the five statements matches the data. If two had matched, the question would have been faulty — checking every option is what proves the answer, not just stopping at the first one that looks right.

Write down the statement that survived

Only one of the five statements matches the data, so the answer is "Thursday has 4 more cakes than Monday."

Read the scale on the vertical axis

Before reading anything off a chart, check what one square on the frequency axis is worth. Here the numbered ticks go up in equal steps, so the height of a bar is read straight off the axis.

Read the bar for January

The top of the January bar lines up with $8$ on the frequency axis, so there are $8$ visitors for January.

Read the bar for February

The top of the February bar lines up with $11$ on the frequency axis, so there are $11$ visitors for February.

Read the bar for March

The top of the March bar lines up with $5$ on the frequency axis, so there are $5$ visitors for March.

Read the bar for April

The top of the April bar lines up with $12$ on the frequency axis, so there are $12$ visitors for April.

Read the bar for May

The top of the May bar lines up with $11$ on the frequency axis, so there are $11$ visitors for May.

Work out the total

Several of the statements talk about the total, so add all the frequencies: there are $47$ visitors altogether.

Note the biggest and the smallest bar

Statements about "the most" and "the fewest" can be settled straight away: the tallest bar is April and the shortest is March.

Test the statement "January has more visitors than March."

Check it against the data ($\text{January} = 8, \text{March} = 5$). It is true, so this is the correct statement.

Test the statement "May has twice as many visitors as March."

Check it against the data ($\text{March} = 5, \text{May} = 11$). It does not match the data, so this statement is wrong.

Test the statement "January and March have the same number of visitors."

Check it against the data ($\text{January} = 8, \text{March} = 5$). It does not match the data, so this statement is wrong.

Test the statement "The total number of visitors is 45."

Check it against the data (total = 47). It does not match the data, so this statement is wrong.

Test the statement "March has the most visitors."

Check it against the data ($\text{March} = 5$). It does not match the data, so this statement is wrong.

Count how many statements are true

Exactly one of the five statements matches the data. If two had matched, the question would have been faulty — checking every option is what proves the answer, not just stopping at the first one that looks right.

Write down the statement that survived

Only one of the five statements matches the data, so the answer is "January has more visitors than March."

Read the scale on the vertical axis

Before reading anything off a chart, check what one square on the frequency axis is worth. Here the numbered ticks go up in equal steps, so the height of a bar is read straight off the axis.

Read the bar for Comedy

The top of the Comedy bar lines up with $6$ on the frequency axis, so there are $6$ tickets for Comedy.

Read the bar for Action

The top of the Action bar lines up with $4$ on the frequency axis, so there are $4$ tickets for Action.

Read the bar for Horror

The top of the Horror bar lines up with $6$ on the frequency axis, so there are $6$ tickets for Horror.

Read the bar for Cartoon

The top of the Cartoon bar lines up with $3$ on the frequency axis, so there are $3$ tickets for Cartoon.

Read the bar for Drama

The top of the Drama bar lines up with $8$ on the frequency axis, so there are $8$ tickets for Drama.

Work out the total

Several of the statements talk about the total, so add all the frequencies: there are $27$ tickets altogether.

Note the biggest and the smallest bar

Statements about "the most" and "the fewest" can be settled straight away: the tallest bar is Drama and the shortest is Cartoon.

Test the statement "Horror has twice as many tickets as Cartoon."

Check it against the data ($\text{Horror} = 6, \text{Cartoon} = 3$). It is true, so this is the correct statement.

Test the statement "Action has 3 more tickets than Horror."

Check it against the data ($\text{Action} = 4, \text{Horror} = 6$). It does not match the data, so this statement is wrong.

Test the statement "Cartoon has the most tickets."

Check it against the data ($\text{Cartoon} = 3$). It does not match the data, so this statement is wrong.

Test the statement "Cartoon and Drama have the same number of tickets."

Check it against the data ($\text{Cartoon} = 3, \text{Drama} = 8$). It does not match the data, so this statement is wrong.

Test the statement "The total number of tickets is 30."

Check it against the data (total = 27). It does not match the data, so this statement is wrong.

Count how many statements are true

Exactly one of the five statements matches the data. If two had matched, the question would have been faulty — checking every option is what proves the answer, not just stopping at the first one that looks right.

Write down the statement that survived

Only one of the five statements matches the data, so the answer is "Horror has twice as many tickets as Cartoon."

Say what is known and what is not

The table has a gap where the City frequency should be, but the total is given, so the gap can be filled by subtraction.

Write down the frequencies that ARE given

These are the rows the table does show.

Add the known frequencies

The rows that are filled in account for $13$ goals.

Use the fact that the rows must add to the total

Every one of the $25$ goals is in exactly one row, so the missing frequency plus $13$ must come to $25$.

Solve for the missing frequency

Subtracting gives $12$, so there are $12$ goals for City.

Fill the gap in the table

The table is now complete and every later step can use it.

Check the completed table

Adding the completed column gives $25$, which matches the total in the question.

Say what the percentage is out of

A percentage is always out of the whole data set, which is all $25$ goals — not out of the $13$ that were already in the table.

Write the amount as a fraction of the total

"$12$ out of $25$" is the fraction $\frac{12}{25}$.

Simplify the fraction

Dividing top and bottom by $1$ gives $\frac{12}{25}$.

Turn the fraction into a percentage

A percentage is a fraction out of $100$, so multiply by $100$.

Do the multiplication

$1200 \div 25 = 48$.

Check by reversing the calculation

$48\%$ of $25$ gives back $12$, the missing frequency, so the percentage is right.

Check the percentages of all the rows

Doing the same for every row gives percentages that add up to $100\%$, as they must.

State the answer

So $48\%$ of the goals are for City.

Say what is known and what is not

The table has a gap where the Black frequency should be, but the total is given, so the gap can be filled by subtraction.

Write down the frequencies that ARE given

These are the rows the table does show.

Add the known frequencies

The rows that are filled in account for $33$ cars.

Use the fact that the rows must add to the total

Every one of the $50$ cars is in exactly one row, so the missing frequency plus $33$ must come to $50$.

Solve for the missing frequency

Subtracting gives $17$, so there are $17$ cars for Black.

Fill the gap in the table

The table is now complete and every later step can use it.

Check the completed table

Adding the completed column gives $50$, which matches the total in the question.

Say what the percentage is out of

A percentage is always out of the whole data set, which is all $50$ cars — not out of the $33$ that were already in the table.

Write the amount as a fraction of the total

"$17$ out of $50$" is the fraction $\frac{17}{50}$.

Simplify the fraction

Dividing top and bottom by $1$ gives $\frac{17}{50}$.

Turn the fraction into a percentage

A percentage is a fraction out of $100$, so multiply by $100$.

Do the multiplication

$1700 \div 50 = 34$.

Check by reversing the calculation

$34\%$ of $50$ gives back $17$, the missing frequency, so the percentage is right.

Check the percentages of all the rows

Doing the same for every row gives percentages that add up to $100\%$, as they must.

State the answer

So $34\%$ of the cars are for Black.