Mini Minds Hub · Free printable
Cumulative Frequency: Free Printable Worksheet for Year 9
- ForYear 9
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Cumulative Frequency is a free printable maths worksheet for Year 9 (ages 13 to 14), in Key Stage 3. Students fill in a frequency table by building the running total, then use it to find the class that holds the median. It takes about 15 minutes, needs only a pencil, and page 2 gives the grown-up notes, help ideas, a stretch task and the answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to the student and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Students complete a table with three columns: time t in minutes, frequency and cumulative frequency. They build the running total one row at a time. Then they use it to answer numbered questions, with space to write. The questions ask which class holds the median, which is the 20th value, and how many students take 30 minutes or less.
- Time t (minutes)
- Frequency
- Cumulative frequency
- Which class holds the median (the 20th value)?
- How many students take 30 minutes or less?
A worked example with different data
22 students time how long they spend on a puzzle, t minutes. The frequencies for the classes 0 < t ≤ 4, 4 < t ≤ 8, 8 < t ≤ 12 and 12 < t ≤ 16 are 3, 6, 8 and 5. Fill in the cumulative frequency column. How many students take 8 minutes or less?
This example uses different numbers from the sheet. It shows how to build the column and how to check it.
Method 1: add down the column- The first cumulative frequency is the same as the first frequency: 3.
- Add the next frequency to the total above: 3 + 6 = 9.
- Add the next one: 9 + 8 = 17.
- Add the last one: 17 + 5 = 22.
- The row for 4 < t ≤ 8 has a running total of 9. That is the number of students who take 8 minutes or less.
- Add all the frequencies: 3 + 6 + 8 + 5 = 22. The last cumulative frequency should match this.
- Take the last frequency from the last total: 22 − 5 = 17.
- 17 matches the row above, so the column is correct.
How the running total is built
Start with the first row
The first cumulative frequency is the same as the first frequency. Nothing comes before it, so there is nothing to add.
Add the next frequency
Each new cumulative frequency is the one above plus the frequency in that row. Say each sum aloud as you write it.
Check the last total
The last cumulative frequency is the number of values altogether. On this sheet the last total should be 40.
Read the column
A cumulative frequency tells you how many values are in that class or in the classes before it. That is why it helps with questions about 'or less'.
Why a running total is useful
A frequency table shows how many values fall in each class. A cumulative frequency table adds them up as it goes, so each row tells you how many values are at or below the top of that class. The running total only ever stays the same or goes up, and it ends at the total number of values.
Once the column is built, it is easier to answer questions about position. To find the class holding the median, find the position of the middle value, then look for the first row where the running total reaches that position. The same idea works for quartiles. Plotting each total against the top of its class gives the cumulative frequency curve.
Skills and curriculum link
- Cumulative frequency
- Reading frequency tables
- Interpreting data
- Finding the median class
- Checking totals
Ideas to help students on the sheet
- Start at the topThe first row is the easiest. Copy the first frequency, then move down one row at a time.
- Use 'so far'Read each cumulative frequency as 'how many so far'. This stops students from copying the frequency column by mistake.
- Check the endThe final total should match the number of values in the whole data set. If it does not, recheck the sums from the top.
- Think about positionFor the median, ask 'which value is in the middle?' first. Then look down the cumulative column to see where that position is reached.
Key words
- FrequencyHow many times a value, or a value in a class, appears in the data.
- Cumulative frequencyA running total of the frequencies, adding each new row to all the rows above.
- ClassA group of values, such as all the times between two limits.
- MedianThe middle value when the data is in order.
- QuartileA value that splits ordered data into quarters. The lower and upper quartiles sit a quarter and three quarters of the way through.
- Running totalA total that grows as each new amount is added to the sum so far.
How to use it
- Print both pages. Page 1 is for the student. Keep page 2, which has the notes and answers.
- Read the table together. Ask what the frequency column tells you and what the cumulative column will tell you.
- Let the student fill in the cumulative frequency column, adding each frequency to the total above and saying each sum aloud.
- Check that the last total equals 40, then answer the questions about the median class and the number of students.
- Check with page 2 and ask, 'How did you decide?' If you like, plot each total against the top of its class on squared paper. Come back another day to repeat it.
Help, stretch and game ideas
If it feels too hard
Add each frequency to the running total from the row above, and say each sum aloud. Cover the rows below with a ruler so only one step shows at a time. Check that the last total equals 40 before moving on to the questions.
To stretch confident children
Plot each cumulative total against the top of its class on squared paper and join the points to draw the curve. Then read off the median from the curve. Next, find the lower and upper quartiles at the 10th and 30th values.
Make it a game
Collect real data, such as arm spans of family or class members. Agree the classes first, tally the results, then build a cumulative frequency table together. Take turns to ask a question about the data that the running total can answer.
Mistakes to watch for
Watch forThe student copies the frequency column into the cumulative column.
Try thisAsk them to read each cumulative number as 'how many so far'. Show that the second row must include the first row as well.
Watch forThe student adds up the cumulative column, or adds a frequency to the wrong row.
Try thisRemind them that each cumulative number already holds everything above it. They only add the new frequency to the total directly above.
Watch forThe student picks the class with the biggest frequency as the median class.
Try thisAsk, 'In which row does the running total first reach the position of the median?' The biggest frequency does not decide it.
Talk about it
- What does the cumulative frequency in a row tell us?
- Why must the last total match the number of values altogether?
- Why can a cumulative frequency never go down as you move down the table?
- How can you find the middle value without listing every value in order?
- What kind of real data could we collect and put in a table like this?
- How did you check your column before you moved on to the questions?
Take it off the page
Family timings
Ask family members how long they take to get ready in the morning. Write the times, sort them into classes and build a cumulative frequency table.
Paper strip tally
Measure hand spans of friends or family with a ruler. Tally them in classes on paper, then add a running total beside the tally.
Plot it by hand
Draw axes on squared paper. Plot a small set of cumulative totals against the top of each class and join the points with a ruler.
Who it is for
Parents
Sit with your student for the first go and let them lead. About 15 minutes is plenty. If they are stuck, ask them to say each running total sum aloud and to check that the final total matches the number of values.
Teachers
Use it as a starter, a plenary after teaching grouped data, a homework task or an early finisher activity. The plotting idea gives a clear extension for confident students. It needs no preparation beyond printing.
Home educators
Print it as part of a wider maths plan. It fits well with a data collecting project, such as timing everyday tasks. Because it is free to print, you can reuse it for revision a few weeks later.
Where this fits
Before this, students meet frequency tables, tally charts and averages. They need to be comfortable adding in order and reading a table carefully. Knowing what the median means makes the final questions easier.
After this, students can draw and read cumulative frequency curves, estimate the median and quartiles and compare distributions. Many students meet these ideas again in Key Stage 4 statistics, so careful practice with the running total now is a good foundation.
Questions parents and teachers ask
- What age is Cumulative Frequency for?
It is written for Year 9 (ages 13 to 14), in Key Stage 3. It suits students who can read a frequency table and are ready to build a running total and use it to find the median class.
- What will students practise?
They build a cumulative frequency column from a frequency table. They then use it to find the class holding the median and to say how many students take 30 minutes or less.
- How long does it take?
It takes about 15 minutes. Students who plot the curve on squared paper afterwards will need a little longer. Page 2 gives a stretch idea for confident students.
- What if it feels too hard?
Slow down and add one row at a time. Add each frequency to the running total from the row above and say each sum aloud. Check that the last total equals 40 before answering the questions.
- Do students have to draw the curve?
No. Plotting is an optional extension. After completing the table, students can plot each cumulative total against the top of its class on squared paper. Page 2 suggests how to take it further.
- Is it free and screen free?
Yes. It is free to print for home and classroom use. It needs only paper and a pencil, so it works for quiet time, homework or a rainy afternoon. Black and white printing is fine.
- Can teachers and home educators use it?
Yes. Teachers can use it as a starter, plenary, early finisher task or homework. Home educators and tutors can use it alone or in a wider plan, and reprint it for revision or for brothers and sisters.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.