Comparing groups of different sizes
Comparing groups of different sizes
When groups differ in size, you compare them by relative frequency, not by frequency.
In the two-way table of 7A and 7B: 10 pupils of 7A walk to school, and 12 of 7B. But 7A has 25 pupils, and 7B has 40:
- In 7A: of the class walk.
- In 7B: of the class walk.
- 7B has more pupils who walk, but in 7A they are a larger part of the class.
To compare the two classes on every answer, divide each cell by its row’s total:
| Walk | Bus | Bike | Car | Total | |
|---|---|---|---|---|---|
| 7A | 40% | 32% | 16% | 12% | 100% |
| 7B | 30% | 40% | 15% | 15% | 100% |
- Each row adds up to 100%: it is the whole class.
- Now the comparison is fair. A larger part of 7B comes by bus (40% against 32%), and by bike – almost the same part (16% and 15%).
The same table as a double bar chart, in percent:
In the chart of the frequencies 7B’s bar was taller for every answer, because 7B has more pupils. In the chart of percentages each class is measured by its own size, and for walking 7A is higher.
A headline: “300 bikes were stolen in town A last year, and only 60 in town B!”
It looks as if far more bikes are stolen in town A. But town A has 30,000 bikes, and town B has 4,000:
- In town A, of the bikes were stolen.
- In town B, of the bikes were stolen.
- In fact a larger part of the bikes was stolen in town B.
The football club has 24 children, and 6 of them are girls.
The swimming club has 30 children, and 9 of them are girls.
What part of the football club are girls? Write it as a percentage.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
What part of the swimming club are girls? Write it as a percentage.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Which club has more girls? In which club is the girls’ part larger?
The pupils of two classes were asked whether they read books in the holidays:
| Yes | No | Total | |
|---|---|---|---|
| 7C | 18 | 12 | 30 |
| 7D | 15 | 5 | 20 |
What part of class 7C said “yes”? Write it as a percentage.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
What part of class 7D said “yes”? Write it as a percentage.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Gil says: “7C reads more, because 18 pupils there said yes.”
Is Gil right? Explain.
Oranim school has 400 pupils, and 30% of them come by bike.
Hadar school has 200 pupils, and 45% of them come by bike.
How many pupils come to Oranim by bike?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
How many pupils come to Hadar by bike?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Which school needs more places for bikes? In which school does a larger part of the pupils come by bike?
A headline: “Herzl Street had 12 road accidents this year, and Rose Lane only 2. Rose Lane is safer!”
Which data are missing to decide which street is safer to drive on? Explain.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power