Year 5StatisticsDeveloping knowledge from dataYear 5 Maths

Collecting data: rounding rules and paired variables

What this lesson covers

  • Measurements for continuous numerical data need to have the place value for rounding specified (e.g. to the nearest centimetre).
  • Bivariate data is data in a set that has two variables for each subject (e.g. dislikes and gender for each student).
Key idea

Data does not arrive. Somebody collects it.

  • And the choices made while collecting decide what you can find out.
  • There are two of them, and neither can be fixed later.
  • How precisely you measure, and whether you record the pairing.
both are made before you write anything down
decisionif you get it wrong
how precisely to measurethe set does not agree with itself
what to pair togethera question becomes unanswerable
Key idea

Continuous data comes from measuring

  • Counting gives whole numbers: 12 children, 3 dogs.
  • Measuring does not. A height can be any value in a range.
  • Here are seven real heights, in centimetres.
Continuous data comes from measuring
Key idea

The rounding is agreed first

  • The curriculum says the place value must be specified.
  • Specified, not just done. That is a claim about the order.
  • You agree the rule before anybody picks up a tape measure.
one girl, three heights, and no set at all
who measurestheir rulewhat they write down
firstnearest cm144 cm
secondnearest mm143.6 cm
thirdnearest 10 cm140 cm
Key idea

Why afterwards is too late

  • You can always round a fine measurement more coarsely.
  • You can never get back millimetres you did not write down.
  • So the rule goes in the plan, and next to the data.
rounding only ever goes one way
you recordedcan you getto the nearest cm?
143.6 cmyes144 cm
140 cmnoit could be 136 to 144
Worked example

Applying the rule

  • To the nearest centimetre: look at the millimetres.
  • 143.6 is past halfway between 143 and 144.
  • So it is recorded as 144 cm.
Applying the rule
Worked example

What the rule does to the whole set

  • Apply it to all seven, and the dots land on whole numbers.
  • Three of them are now the same value: 141.
  • You lost detail. You gained a set you can work with.
What the rule does to the whole set
Key idea

Too precise is also wrong

  • Measuring a field to the nearest millimetre is not careful.
  • It is a lie about how well you measured. The tape sags.
  • Match the precision to what you can actually do.
a sensible rule, not the finest possible one
measuringround towhy
a pencilnearest mma ruler can do it
your heightnearest cmyou move more than a mm
a sports fieldnearest mthe tape sags anyway
Key idea

Two things about each person

  • Bivariate data has two variables for every subject.
  • Here: what each student does at lunchtime, and their gender.
  • One row per student, with both values on that row.
the row is what pairs them
studentat lunchtimegender
Arohasportgirl
Benlibraryboy
Melesportgirl
Tanesportboy
Key idea

The mistake that cannot be undone

  • Tally lunchtime activities. Then tally boys and girls.
  • You have collected both variables, and lost the link.
  • "Do more boys than girls play sport?" is now unanswerable.
two one-variable tallies are not bivariate data
what you havewhat you can ask
12 play sporthow many play sport
12 boys, 15 girlshow many boys there are
both, separatelynothing about the two together
Worked example

Recorded properly, you can ask

  • With the pairing kept, the tally has rows and columns.
  • Now: 7 boys play sport and 5 girls do.
  • And the library is the other way round: 2 boys, 6 girls.
one table, and the questions answer themselves
at lunchtimeboysgirlstotal
sport7512
library268
talking347
Key idea

Both variables here are categories

  • Lunchtime activity is a category, not a number.
  • So is gender. Neither can be averaged or measured.
  • Paired categories are what you count into a two-way table.
the kind decides what you may do with it
variablekindyou can
heightcontinuous numbermeasure and round it
lunchtime activitycategorycount how many
gendercategorycount how many
Key idea

Check it adds up

  • Every subject appears exactly once, in exactly one cell.
  • So the cells must total the number of people you asked.
  • 12 + 8 + 7 is 27. If your class is 27, the table is complete.
both ways round must give the same total
checkvalue
sport + library + talking12 + 8 + 7 = 27
boys + girls12 + 15 = 27
people in the class27
Your turn

Your turn

  • 1. Round 156.4 cm and 156.5 cm to the nearest centimetre.
  • 2. What precision would you use for the length of a room?
  • 3. Name the two variables in "pets owned, and year level".
  • 4. A two-way table totals 24 across and 26 down. What is wrong?
Show answer

1. 156 cm and 157 cm: exactly halfway rounds up. 2. Nearest centimetre, or nearest 10 cm. Millimetres would be pretending. 3. Number of pets (a count) and year level (a category). 4. Someone has been counted twice, or missed. Both totals must match.

Summary

What to take away

  • Agree the rounding before you measure, and record the rule.
  • Bivariate means both values on one row, per subject.
  • A pairing you did not write down cannot be recovered.
the closing chart
jobthe move
continuous dataspecify the place value first
choosing precisionmatch what you can actually measure
two variablesone row per subject, both values
checking a tabletotals must agree both ways

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