Steply

Mean, median, mode, range

Foundations · 27 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Add them all
  2. Count them
  3. Share equally
  4. Check

The steps for Mean of 2, 4, 6. Every solution names its steps, so you always know what comes next.

Worked examples

Mean of 2, 4, 6 Easy

The question

Question: find the mean of 2, 4 and 6.

Mean of 2, 4, 6

The mean is the fair share.

We add them all, then share the total equally.

mean: add them all, then ÷ how many

1 Add them all

We add all the numbers, from left to right.

= 2 + 4 + 6

So the total is 12.

= total = 12

2 Count them

Now we count the numbers.

There are 3.

= how many = 3

3 Share equally

We share the total equally: 12 divided by 3.

= mean = 123

12 divided by 3 is 4.

= mean = 4

4 Check

Let's check: if every number were 4, 3 of them would make 4 times 3.

That is 12, the total.

So it is right!

4 × 3 = 12

Let's look back.

First: add them all.

Then: count them.

Then: share equally.

Last: check.

Answer
= mean = 4

▶ Watch it solved

Mean of 3, 4, 4 Medium

The question

Question: find the mean of 3, 4 and 4.

Mean of 3, 4, 4

The mean is the fair share.

We add them all, then share the total equally.

mean: add them all, then ÷ how many

1 Add them all

We add all the numbers, from left to right.

= 3 + 4 + 4

So the total is 11.

= total = 11

2 Count them

Now we count the numbers.

There are 3.

= how many = 3

3 Share equally

We share the total equally: 11 divided by 3.

= mean = 113

11 divided by 3 does not come out even.

It is 3.6667 and more digits.

11 ÷ 3 = 3.6667…

Rounded to 2 decimal places, the mean is about 3.67.

= mean ≈ 3.67
≈ means about

Let's look back.

First: add them all.

Then: count them.

Last: share equally.

Answer
≈ means about

▶ Watch it solved

Mean of 85, 90, 78, 92, 80 Harder

The question

Question: find the mean of 85, 90, 78, 92 and 80.

Mean of 85, 90, 78, 92, 80

The mean is the fair share.

We add them all, then share the total equally.

mean: add them all, then ÷ how many

1 Add them all

We add all the numbers, from left to right.

= 85 + 90 + 78 + 92 + 80

So the total is 425.

= total = 425

2 Count them

Now we count the numbers.

There are 5.

= how many = 5

3 Share equally

We share the total equally: 425 divided by 5.

= mean = 4255

425 divided by 5 is 85.

= mean = 85

4 Check

Let's check: if every number were 85, 5 of them would make 85 times 5.

That is 425, the total.

So it is right!

85 × 5 = 425

Let's look back.

First: add them all.

Then: count them.

Then: share equally.

Last: check.

Answer
= mean = 85

▶ Watch it solved

Practice

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

Easy

  1. mean of 2, 4, 6
    Answer
    = mean = 4
  2. mean of 5, 8, 6, 9
    Answer
    = mean = 7
  3. median of 3, 9, 4, 7, 5
    Answer
    = median = 5
  4. median of 8, 2, 6
    Answer
    = median = 6
  5. mode of 2, 3, 3, 5, 3, 8
    Answer
    = mode = 3
  6. mode of 7, 1, 7, 4
    Answer
    = mode = 7
  7. range of 4, 9, 2, 7
    Answer
    = range = 7
  8. range of 15, 3, 11, 8, 20
    Answer
    = range = 17
  9. mean of 10, 20, 30, 40, 50
    Answer
    = mean = 30
  10. median of 1, 5, 2, 8, 6, 3
    Answer
    = median = 4

Medium

  1. mean of 3, 4, 4
    Answer
    ≈ means about
  2. mean of 12, 15, 9, 14
    Answer
    = mean = 12.5
  3. median of 6, 1, 9, 4
    Answer
    = median = 5
  4. median of 12, 5, 9, 15, 10, 7
    Answer
    = median = 9.5
  5. mode of 4, 6, 4, 6, 9
    Answer
    = modes = 4 and 6
  6. mode of 1, 2, 3, 4
    Answer
    = no mode
  7. range of 0, 14, 6, 9
    Answer
    = range = 14
  8. mean of 7, 2, 9, 4, 3
    Answer
    = mean = 5
  9. median of 2.5, 1.5, 4, 3
    Answer
    = median = 2.75
  10. mean of 0, 0, 3, 5
    Answer
    = mean = 2

Harder

  1. mean of 85, 90, 78, 92, 80
    Answer
    = mean = 85
  2. median of 13, 7, 8, 20, 11, 9, 4
    Answer
    = median = 9
  3. mode of 3, 5, 5, 4, 5, 3, 2
    Answer
    = mode = 5
  4. range of 2.4, 6.1, 3.8, 0.9
    Answer
    = range = 5.2
  5. mean of -3, 5, 2, -4
    Answer
    = mean = 0
  6. median of 4, -2, 7, -5, 0
    Answer
    = median = 0
  7. range of -3, 8, 2, -6
    Answer
    = range = 14