Grouped data and two-way tables
Grouped data and two-way tables
In grade 6 you put data in a frequency table: for each value, how many times it came up – its frequency. The frequencies add up to the number of all the data.
The 24 pupils of class 7B wrote down how many minutes the way to school takes them:
5, 12, 8, 25, 18, 3, 15, 22, 10, 7, 31, 14, 9, 19, 26, 11, 6, 16, 35, 13, 20, 4, 17, 28
Almost every number comes up only once, and a table with a column for each number would be long and would not tell much. So the data are put in equal groups, of 10 minutes each:
| Time (minutes) | 0–9 | 10–19 | 20–29 | 30–39 |
|---|---|---|---|---|
| Frequency | 7 | 10 | 5 | 2 |
- Each value goes into exactly one group: 10 belongs to 10–19, not to 0–9.
- Now you see at once that the largest group is 10–19 minutes.
- What is lost: from the table alone you cannot tell the longest time – only that it is between 30 and 39 minutes.
The pupils of two classes were asked how they get to school. To see both classes together, the answers go into a two-way table: a row for each class, and a column for each answer.
| Walk | Bus | Bike | Car | Total | |
|---|---|---|---|---|---|
| 7A | 10 | 8 | 4 | 3 | 25 |
| 7B | 12 | 16 | 6 | 6 | 40 |
| Total | 22 | 24 | 10 | 9 | 65 |
- Each cell counts pupils who fit two things at once: 8 pupils are in class 7A and come by bus.
- A row’s sum is the number of pupils in the class: in 7A – 25.
- A column’s sum is the number of pupils in both classes who gave that answer: 24 pupils come by bus.
- In the corner – the number of all the pupils, 65. You get it both by adding the last row and by adding the last column, and so check the working.
A two-way table is drawn as a double bar chart: two bars for each answer, one for each class.
- For every answer 7B’s bar is taller. That does not mean 7B’s pupils prefer every way: 7B simply has more pupils, 40 against 25.
- To compare the classes, look at what part of each class gave each answer – the relative frequency.
The points Ella scored in each basketball game this season:
14, 8, 21, 17, 5, 12, 19, 25, 9, 16, 11, 23, 18, 7, 15, 20
Put the data in groups: 0–9, 10–19, 20–29.
In how many games did Ella score 10–19 points?
/ – 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
In how many games did Ella score 20 points or more?
/ – 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
Can you tell from the table of groups alone in how many games Ella scored exactly 15 points? Explain.
The grade 7 pupils were asked whether they have a pet. A few numbers are missing from the table:
| Have | Have not | Total | |
|---|---|---|---|
| Boys | 18 | ? | 40 |
| Girls | ? | 21 | ? |
| Total | 42 | ? | 85 |
How many boys have no pet?
/ – 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 girls are there in the grade?
/ – 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 in the grade have no pet?
/ – 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
The chart shows the favourite sport of the pupils of 7C and 7D.
How many pupils are there in 7C?
/ – 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 more pupils chose basketball in 7D than in 7C?
/ – 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
/ – 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