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Frequency tables

Foundations · 21 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. List the values
  2. Tally
  3. Count
  4. Check

The steps for Frequency table of 2, 3, 3, 1, 2, 3. Every solution names its steps, so you always know what comes next.

Worked examples

Frequency table of 2, 3, 3, 1, 2, 3 Easy

The question

Question: make a frequency table of 2, 3, 3, 1, 2 and 3.

2, 3, 3, 1, 2, 3

The frequency of a number is how many times it comes.

frequency f = how many times

1 List the values

We write each value once, smallest first: 1, 2 and 3.

2 Tally

Careful!

Cross out each number as you count it.

Then none is missed, and none is counted twice.

Careful: cross out each number as you count it

The first number is 2.

We cross it out, and put one mark next to 2.

Next is 3: one mark next to 3.

And so on: one mark for each number.

Every number is crossed out.

So every number has its mark.

3 Count

1 has 1 mark: f = 1.

2 has 2 marks: f = 2.

3 has 3 marks: f = 3.

4 Check

Let's check.

We add the f column: 1 + 2 + 3 = 6.

There are 6 numbers in the list.

Every one is counted.

So it is right!

1 + 2 + 3 = 6 numbers

Let's look back.

First: list the values.

Then: tally.

Then: count.

Last: check.

Answer
2, 3, 3, 1, 2, 3

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Frequency table of 4, 6, 5, 4, 6, 6, 3, 5, 6, 6, 4 Medium

The question

Question: make a frequency table of 4, 6, 5, 4, 6, 6, 3, 5, 6, 6 and 4.

4, 6, 5, 4, 6, 6, 3, 5, 6, 6, 4

The frequency of a number is how many times it comes.

frequency f = how many times

1 List the values

We write each value once, smallest first: 3, 4, 5 and 6.

2 Tally

Careful!

Cross out each number as you count it.

Then none is missed, and none is counted twice.

Careful: cross out each number as you count it

The first number is 4.

We cross it out, and put one mark next to 4.

Next is 6: one mark next to 6.

And so on: one mark for each number.

The fifth mark goes across the other four.

That makes a group of 5, easy to count.

Every number is crossed out.

So every number has its mark.

3 Count

3 has 1 mark: f = 1.

4 has 3 marks: f = 3.

5 has 2 marks: f = 2.

6 has 5 marks: f = 5.

4 Check

Let's check.

We add the f column: 1 + 3 + 2 + 5 = 11.

There are 11 numbers in the list.

Every one is counted.

So it is right!

1 + 3 + 2 + 5 = 11 numbers

Let's look back.

First: list the values.

Then: tally.

Then: count.

Last: check.

Answer
4, 6, 5, 4, 6, 6, 3, 5, 6, 6, 4

▶ Watch it solved

Frequency table of 3, 1, 4, 1, 5, 2, 6, 5, 3, 5, 1, 4, 5, 2, 5 Harder

The question

Question: make a frequency table of 3, 1, 4, 1, 5, 2, 6, 5, 3, 5, 1, 4, 5, 2 and 5.

3, 1, 4, 1, 5, 2, 6, 5, 3, 5, 1, 4, 5, 2, 5

The frequency of a number is how many times it comes.

frequency f = how many times

1 List the values

We write each value once, smallest first: 1, 2, 3, 4, 5 and 6.

2 Tally

Careful!

Cross out each number as you count it.

Then none is missed, and none is counted twice.

Careful: cross out each number as you count it

The first number is 3.

We cross it out, and put one mark next to 3.

Next is 1: one mark next to 1.

And so on: one mark for each number.

The fifth mark goes across the other four.

That makes a group of 5, easy to count.

Every number is crossed out.

So every number has its mark.

3 Count

1 has 3 marks: f = 3.

2 has 2 marks: f = 2.

And the same for the rest.

4 Check

Let's check.

We add the f column: 3 + 2 + 2 + 2 + 5 + 1 = 15.

There are 15 numbers in the list.

Every one is counted.

So it is right!

3 + 2 + 2 + 2 + 5 + 1 = 15 numbers

Let's look back.

First: list the values.

Then: tally.

Then: count.

Last: check.

Answer
3, 1, 4, 1, 5, 2, 6, 5, 3, 5, 1, 4, 5, 2, 5

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. frequency table of 2, 3, 3, 1, 2, 3
    Answer
    2, 3, 3, 1, 2, 3
  2. frequency table of 5, 6, 5, 7, 6, 5, 5
    Answer
    5, 6, 5, 7, 6, 5, 5
  3. frequency table of 1, 2, 2, 3, 1, 2, 4, 2
    Answer
    1, 2, 2, 3, 1, 2, 4, 2
  4. frequency table of 0, 1, 1, 2, 0, 1, 3, 1, 1
    Answer
    0, 1, 1, 2, 0, 1, 3, 1, 1
  5. mean of the frequency table x: 1, 2, 3; f: 2, 3, 5
    Answer
    1 decimal place: 1 more than the data
  6. mean of the frequency table x: 2, 4, 6; f: 1, 2, 1
    Answer
    mean = 4
  7. mean of the frequency table x: 10, 20, 30; f: 3, 4, 3
    Answer
    mean = 20
  8. mean of the frequency table x: 1, 2, 3, 4; f: 4, 3, 2, 1
    Answer
    mean = 2

Medium

  1. frequency table of 4, 6, 5, 4, 6, 6, 3, 5, 6, 6, 4
    Answer
    4, 6, 5, 4, 6, 6, 3, 5, 6, 6, 4
  2. frequency table of 12, 15, 12, 13, 15, 15, 14, 12, 15, 13
    Answer
    12, 15, 12, 13, 15, 15, 14, 12, 15, 13
  3. frequency table of 7, 8, 8, 9, 7, 8, 10, 8, 9, 8, 8, 7
    Answer
    7, 8, 8, 9, 7, 8, 10, 8, 9, 8, 8, 7
  4. mean of the frequency table x: 1, 2, 3, 4; f: 3, 5, 8, 4
    Answer
    1 decimal place: 1 more than the data
  5. mean of the frequency table x: 0, 1, 2, 3; f: 5, 8, 4, 3
    Answer
    1 decimal place: 1 more than the data
  6. mean of the frequency table x: 5, 6, 7, 8; f: 2, 6, 7, 5
    Answer
    1 decimal place: 1 more than the data
  7. mean of the frequency table x: 2, 3, 4, 5, 6; f: 1, 4, 6, 5, 4
    Answer
    1 decimal place: 1 more than the data
  8. mean of the frequency table x: 0, 1, 2; f: 6, 3, 1
    Answer
    1 decimal place: 1 more than the data

Harder

  1. frequency table of 3, 1, 4, 1, 5, 2, 6, 5, 3, 5, 1, 4, 5, 2, 5
    Answer
    3, 1, 4, 1, 5, 2, 6, 5, 3, 5, 1, 4, 5, 2, 5
  2. mean of the frequency table x: 1, 2, 3, 4, 5; f: 2, 5, 9, 6, 3
    Answer
    1 decimal place: 1 more than the data
  3. mean of the frequency table x: 1.5, 2.5, 3.5; f: 2, 5, 3
    Answer
    mean = 2.6
  4. mean of the frequency table x: 0, 1, 2, 3; f: 7, 9, 5, 3
    Answer
    1 decimal place: 1 more than the data
  5. mean of the frequency table x: 4, 5, 6; f: 5, 10, 5
    Answer
    mean = 5