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Calculate an arithmetic mean

Find the mean of a short supplied data set.

Watch the worked example

The Mean: A Fair Share

This video shows how to add a set of values and divide by how many there are to find the mean average. Watch an 11+ maths question solved step by step.

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Quick quiz: Calculate an arithmetic mean

10 questions, with feedback after each one. No sign-up needed.

Read the questions in this quiz
  1. Question 1

    What is the mean of the Senior dancers column?

    Folk
    Junior dancers
    254
    Senior dancers
    455
    Breakdance
    Junior dancers
    235
    Senior dancers
    560
    Swing
    Junior dancers
    646
    Senior dancers
    272
    Ballet
    Junior dancers
    219
    Senior dancers
    191
    Flamenco
    Junior dancers
    519
    Senior dancers
    602
    Salsa
    Junior dancers
    263
    Senior dancers
    410
    • A.415
    • B.498
    • C.191
    • D.602
  2. Question 2

    What is the mean of the April loads column?

    Rubble
    April loads
    593
    October loads
    692
    Cardboard
    April loads
    356
    October loads
    770
    Timber
    April loads
    228
    October loads
    165
    Textiles
    April loads
    251
    October loads
    465
    Compost
    April loads
    204
    October loads
    199
    Batteries
    April loads
    780
    October loads
    275
    • A.492
    • B.780
    • C.402
    • D.204
  3. Question 3

    What is the mean of the October bags column?

    Cartons
    May bags
    202
    October bags
    683
    Glass
    May bags
    215
    October bags
    185
    Driftwood
    May bags
    635
    October bags
    159
    Rope
    May bags
    584
    October bags
    322
    Plastic
    May bags
    427
    October bags
    759
    Netting
    May bags
    622
    October bags
    724
    • A.472
    • B.159
    • C.459
    • D.759
  4. Question 4

    What is the mean of the July bookings column?

    Hilltop
    June bookings
    793
    July bookings
    608
    Orchard
    June bookings
    670
    July bookings
    691
    Copse
    June bookings
    232
    July bookings
    89
    Meadow
    June bookings
    689
    July bookings
    675
    Woodland
    June bookings
    694
    July bookings
    66
    Paddock
    June bookings
    545
    July bookings
    523
    • A.691
    • B.2652
    • C.66
    • D.442
  5. Question 5

    What is the mean of the Morning sightings column?

    Meerkats
    Morning sightings
    367
    Afternoon sightings
    102
    Bison
    Morning sightings
    774
    Afternoon sightings
    370
    Lemurs
    Morning sightings
    740
    Afternoon sightings
    678
    Otters
    Morning sightings
    715
    Afternoon sightings
    87
    Wolves
    Morning sightings
    287
    Afternoon sightings
    737
    Tapirs
    Morning sightings
    711
    Afternoon sightings
    74
    • A.287
    • B.774
    • C.599
    • D.3594
  6. Question 6

    What is the mean of the December parcels column?

    Wales
    November parcels
    701
    December parcels
    376
    Devon
    November parcels
    742
    December parcels
    321
    Yorkshire
    November parcels
    668
    December parcels
    369
    Scotland
    November parcels
    699
    December parcels
    596
    Cornwall
    November parcels
    643
    December parcels
    622
    Norfolk
    November parcels
    546
    December parcels
    410
    • A.622
    • B.321
    • C.2694
    • D.449
  7. Question 7

    What is the mean of the North plot trees column?

    Birch
    North plot trees
    381
    South plot trees
    613
    Rowan
    North plot trees
    195
    South plot trees
    277
    Alder
    North plot trees
    787
    South plot trees
    265
    Beech
    North plot trees
    53
    South plot trees
    145
    Oak
    North plot trees
    52
    South plot trees
    428
    Hazel
    North plot trees
    752
    South plot trees
    365
    • A.52
    • B.787
    • C.444
    • D.370
  8. Question 8

    What is the mean of the Evening passengers column?

    Garndale
    Morning passengers
    528
    Evening passengers
    166
    Denholm
    Morning passengers
    110
    Evening passengers
    672
    Bridgend
    Morning passengers
    102
    Evening passengers
    329
    Caldale
    Morning passengers
    203
    Evening passengers
    181
    Ashford
    Morning passengers
    163
    Evening passengers
    670
    Eastwick
    Morning passengers
    355
    Evening passengers
    310
    • A.388
    • B.419
    • C.166
    • D.672
  9. Question 9

    What is the mean of the March crates column?

    Handbags
    January crates
    73
    March crates
    87
    Curtains
    January crates
    709
    March crates
    184
    Crockery
    January crates
    237
    March crates
    689
    Clothes
    January crates
    751
    March crates
    83
    Puzzles
    January crates
    387
    March crates
    247
    Records
    January crates
    315
    March crates
    570
    • A.83
    • B.689
    • C.310
    • D.372
  10. Question 10

    What is the mean of the Saturday boxes column?

    Hutches
    Saturday boxes
    147
    Sunday boxes
    370
    Collars
    Saturday boxes
    635
    Sunday boxes
    614
    Chews
    Saturday boxes
    247
    Sunday boxes
    94
    Kibble
    Saturday boxes
    478
    Sunday boxes
    457
    Bedding
    Saturday boxes
    358
    Sunday boxes
    107
    Leads
    Saturday boxes
    673
    Sunday boxes
    672
    • A.673
    • B.410
    • C.147
    • D.423

Practise it now

5 classmates stacked up their reading tokens into towers. Time to make sense of the piles.

It covers most of this skill rather than all of it.

Loading the interactive exercise. Nothing you do here is saved or scored.

A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Working out a mean from a table

What is the mean of the Saturday cups column?

Drinks poured at the park cafe.

Cocoa
Saturday cups
46
Sunday cups
48
Lemonade
Saturday cups
67
Sunday cups
25
Cordial
Saturday cups
61
Sunday cups
8
Milkshake
Saturday cups
46
Sunday cups
56

Data table with columns Drink, Saturday cups, Sunday cups. Rows: Drink Cocoa, Saturday cups 46, Sunday cups 48; Drink Lemonade, Saturday cups 67, Sunday cups 25; Drink Cordial, Saturday cups 61, Sunday cups 8; Drink Milkshake, Saturday cups 46, Sunday cups 56.

Table columns: Drink, Saturday cups, Sunday cups. Rows: Cocoa, 46, 48; Lemonade, 67, 25; Cordial, 61, 8; Milkshake, 46, 56.

  1. 220
  2. 55
  3. 46
  4. 67

Answer: 55

How you get there

The Saturday cups column adds up to 220 across 4 rows, and 220 shared between 4 is 55, which means the mean is not any single row's figure.

Why the other answers tempt

The middle of the largest and smallest values is the range midpoint, not the mean.

If they are stuck, say this

Add every number in the Saturday cups column first, then share that total equally between the 4 rows.

Now do it live in Fair Share Machine

How each of these 2 exercises teaches it

Fair Share Machine

5 classmates stacked up their reading tokens into towers. Time to make sense of the piles.

Sharing the blocks out equally leaves every tower at 5 - that levelled height IS the mean (8+5+6+3+3=25, shared between 5). The height that appears most often is 3: that is the mode.

  1. Step 1. Share it out. Move blocks between the towers until every tower is the same height.
  2. Step 2. Find the crowd. Tap every tower that shares the most common height.

What to say if they get stuck

  1. Nothing is added or taken away - blocks only ever move from one tower to another.
  2. The mean is the height every tower reaches once the sharing is fair.
  3. Median means middle, mode means most, range means the gap from shortest to tallest.

Open Fair Share Machine on its own page to share it

Average Showdown

Only one of the two claims is true about these block towers. Tap the true one.

Mean, median and mode are three different questions, so they usually give three different answers. The mean shares every block out equally, so add the towers up and divide by how many towers there are. The median is about position, not size: sort the towers, then point at the middle one. The mode is about how often, so look for the height that repeats. When a claim looks wrong, work out the statistic it names before you decide, because most mistakes come from checking the wrong one.

What to say if they get stuck

  1. The median is the middle tower once you put them in order from smallest to tallest.
  2. The mean is what every tower would be if you shared all the blocks out equally.
  3. The mode is the height that turns up more often than any other.

Open Average Showdown on its own page to share it

Related maths skills

All maths 11+ skills

Questions parents ask about calculate an arithmetic mean

What this skill involves, common mistakes and ways to practise it at home.

Find the mean of a short supplied data set. It is one of 55 named maths skills in the 11+, in the data strand, and this page carries 2 interactive exercises that practise it.

Knowing which maths topic to practise is most of the work

A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.