Choosing the best average

The Maths Habit

Find the median and the mean.

1, 2, 6median 2
mean 3
3, 4, 8median 4
mean 5
2, 5, 5median 5
mean 4

One dot is not like the others.
Which one? Why?

ABCDEE. It is far away from the rest.

Average
One number that describes a whole group of data.
median and mean
Outlier
A value much bigger or much smaller than the rest.
Mode
The value you see most often.
dogcatdogfish

medianmeanThe outlier pulls the mean.Better: the median
  1. 1Find the median and the mean.Cross off to the middle. Share the total equally.
  2. 2Look for an outlier.A value far away from the rest.
  3. 3Pick the better average.An outlier: use the median.
    No outlier: use the mean.

Which average describes the group better?

051015Goals for 5 players
1, 3, 3, 4, 14
1Find the median and the mean.
Median3
Mean25÷5=5
2Look for an outlier.
an outlierno outlier
3Pick the better average.
Better:meanmedian

Which average describes the group better?

012345678910Pets owned by 5 friends
4, 6, 7, 8, 10
1Find the median and the mean.
Median7
Mean35÷5=7
2Look for an outlier.
an outlierno outlier
3Pick the better average.
Better:meanmedian

Which average describes the group better?

051015Goals for 5 players
1, 3, 3, 4, 14
1Find the median and the mean.
Median3
Mean25÷5=5
2Look for an outlier.
an outlierno outlier
3Pick the better average.
Better:meanmedian
1Find the median and the mean.2Look for an outlier.3An outlier: median. No outlier: mean.

Which average describes the group better?

05101520Texts sent by 5 friends
2, 3, 4, 4, 17
1Find the median and the mean.
Median4
Mean30÷5=6
2Look for an outlier.
an outlierno outlier
3Pick the better average.
Better:meanmedian

Which average describes the group better?

051015Goals for 5 players
1, 3, 3, 4, 14
1Find the median and the mean.
Median3
Mean25÷5=5
2Look for an outlier.
an outlierno outlier
3Pick the better average.
Better:meanmedian
1Find the median and the mean.2Look for an outlier.3An outlier: median. No outlier: mean.

Which average describes the group better?

051015Quiz scores for 5 students
2, 10, 11, 11, 11
1Find the median and the mean.
Median11
Mean45÷5=9
2Look for an outlier.
an outlierno outlier
3Pick the better average.
Better:meanmedian

Which average describes the group better?

051015Goals for 5 players
1, 3, 3, 4, 14
1Find the median and the mean.
Median3
Mean25÷5=5
2Look for an outlier.
an outlierno outlier
3Pick the better average.
Better:meanmedian
1Find the median and the mean.2Look for an outlier.3An outlier: median. No outlier: mean.

Which average describes the group better?

012345678910Books read by 5 students
3, 5, 6, 7, 9
1Find the median and the mean.
Median6
Mean30÷5=6
2Look for an outlier.
an outlierno outlier
3Pick the better average.
Better:meanmedian

1Find the median and the mean.2Look for an outlier.3An outlier: median. No outlier: mean.

1Which average describes the group better?

051015Goals
1, 2, 2, 3, 12
Median2
Mean20÷5=4
an outlierno outlier
Better:meanmedian

2Which average describes the group better?

56789101112131415Ages
6, 7, 8, 9, 10
Median8
Mean40÷5=8
an outlierno outlier
Better:meanmedian

3Which average describes the group better?

051015Points
0, 9, 10, 10, 11
Median10
Mean40÷5=8
an outlierno outlier
Better:meanmedian

dogcatdogfishdog
WordsUse the modeIt is dog
  1. 1Numbers or words?Look at the data.
  2. 2Words: use the mode.You cannot add words or put them in order.
  3. 3Find the one you see most.The tallest bar, or the word you count most.

Favourite fruit in a class. Which average can describe this group?

0246810AppleBananaPearGrapeFrequency
1Numbers or words?
numberswords
2Words: use the mode.
meanmedianmode
3Find the one you see most.
It isBanana

Colours of cars in a car park. Which average can describe this group?

0246810RedBlueBlackWhiteFrequency
1Numbers or words?
numberswords
2Words: use the mode.
meanmedianmode
3Find the one you see most.
It isBlack

Favourite fruit in a class. Which average can describe this group?

0246810AppleBananaPearGrapeFrequency
1Numbers or words?
numberswords
2Words: use the mode.
meanmedianmode
3Find the one you see most.
It isBanana
1Numbers or words?2Words: use the mode.3Find the one you see most.

Favourite sports in a club. Which average can describe this group?

0246810DartsGolfRugbyChessFrequency
1Numbers or words?
numberswords
2Words: use the mode.
meanmedianmode
3Find the one you see most.
It isRugby

Favourite fruit in a class. Which average can describe this group?

0246810AppleBananaPearGrapeFrequency
1Numbers or words?
numberswords
2Words: use the mode.
meanmedianmode
3Find the one you see most.
It isBanana
1Numbers or words?2Words: use the mode.3Find the one you see most.

Seven friends choose a snack. Which average can describe this group?

crispsfruitcrispsnutsfruitcrispscake
1Numbers or words?
numberswords
2Words: use the mode.
meanmedianmode
3Find the one you see most.
It iscrisps

Favourite fruit in a class. Which average can describe this group?

0246810AppleBananaPearGrapeFrequency
1Numbers or words?
numberswords
2Words: use the mode.
meanmedianmode
3Find the one you see most.
It isBanana
1Numbers or words?2Words: use the mode.3Find the one you see most.

Drinks sold at lunch. Which average can describe this group?

0246810MilkJuiceWaterTeaFrequency
1Numbers or words?
numberswords
2Words: use the mode.
meanmedianmode
3Find the one you see most.
It isWater

Choosing the best average worksheet, page 1

Choosing the best average worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. For 2, 3, 3, 4, 13, use the mean.

    Wrong: 13 is an outlier

  2. For 5, 6, 7, 8, 9, use the mean.

    Right

  3. For favourite colours, use the median.

    Wrong: use the mode

  4. For 0, 8, 9, 9, 9, use the median.

    Right

  5. For favourite pets, use the mode.

    Right

  1. Find the mean of 18, 20, 21, 22, 22, 23 and 80. Is the median, 22, better?

    29.4; yes

  2. Write five numbers where the mean is bigger than four of them.

    e.g. 1, 2, 2, 3, 12

  3. Four workers earn £30 000. The boss earns £130 000. Is £50 000 a fair average pay?

    No: £30 000

  1. Which average describes 1, 2, 3, 4 and 15 better?

    median
    1, 2, 3, 4, 151Find the medianand the mean.Median3Mean25÷5=52Look foran outlier.an outlierno outlier3Pick the betteraverage.meanmedian

  2. Which average describes 3, 4, 6, 6 and 6 better?

    mean
    3, 4, 6, 6, 61Find the medianand the mean.MedianMean÷=2Look foran outlier.an outlierno outlier3Pick the betteraverage.meanmedian

  3. Which average describes 4, 5, 5, 6 and 30 better? Why?

    the median: 30 is an outlier
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