Statistics

Question 1

What did discrete and continuous data include?

Answer 1

Discrete data - This data is counted and can
only take certain values. E.g. the number of
students in a class (you can’t have half a student).

Continuous data - This data is measured and
can take any value (within a range) E.g. People’s heights could be any value (within the range of human heights), not just certain fixed heights.

Question 2

What are the four stages of handling

data?

Answer 2

1. Collecting
2. Organising
3. Representing
4. Interpreting

Question 3

Pictorial Ways of Representing Data

Answer 3

Venn diagram (not referenced in 2014 Curriculum)

1. Carroll diagram (not referenced in 2014 Curriculum)
2. Pictogram
3. Block graph
4. Bar chart / bar line
5. Line graph
6. Pie charts

Question 4

What is a numerical representation?

Answer 4

Tally charts

Question 5

What is data representing data?

Answer 5

Data is represented using diagrams to make interpretation easier.  To produce a good representation:
• Organise – tally; frequency
• Diagram – choose appropriately!
• Title
• Key (if necessary)
• Scale 
• Label

Question 6

What way is the x axis?

Answer 6

Horizontal

Question 7

What way is the y axis?

Answer 7

Vertical

Question 8

What are bar charts called?

Answer 8

Bar graphs

Question 9

What are bar charts good for?

Answer 9

Are good when your data is in categories such as drama, comedy etc

Question 10

When do you use an histogram?

Answer 10

Histograms are used in continuous data such as peoples height. Then you use histograms.

Question 11

What are the differences between a bar chart and a histogram when you draw them?

Answer 11

You leave gaps in a bar chart not in a histogram.

Question 12

What are line graph points connected together mean?

Answer 12

A graph with points connected by lines to show how something changes in value
As time goes by
Or as something changes

Question 13

What is the best way to do collecting data – sorting data Progression steps

Answer 13

Birthday month 4 corners

Talk about seasonal birthday

Question 14

What are the 2 variables and the 4 sub sets?

Answer 14

Venn Diagram

Carroll Diagram

Question 15

What are the misconceptions in statistics

Answer 15

That all pictograms/ block graphs/ bar charts are vertical.
Position of zero on axis.
Misinterpreting scale & symbols.
Tallying errors
Confusion between data handling and conducting a mathematical investigation

Question 16

What other misconceptions can occur?

Answer 16

Representations of data - Data is presented in this unit using pictograms, bar charts, tables and line graphs. Children will use these structures to draw conclusions and answer questions about data.
Misreading representations of data - Children may misread representations or scales. For example, they may miscount the number of pictogram symbols or their value, or misread the value on the vertical axis of a bar chart, especially where a point falls between two labelled divisions.
Reading continuous data incompletely
Children may think they can read data from only the marked points on the x-axis of a line graph. Address this using targeted questioning, encouraging them to find data for points between two labelled divisions.

Question 17

How can a deeper knowledge be achieved?

Answer 17

To deepen their understanding, give children a variety of statements about a set of data, and ask them to assess which are true and which are false. You could also encourage them to create their own ‘true or false’ statements to challenge a partner.
(On screen: a line graph appears, showing continuous data for temperature against times of day. The following statement appears. ‘The highest temperature was 18°C.’ This is correctly labelled in child’s handwriting as ‘True’. Below this, the following statement appears. ‘The difference between the highest and lowest temperate was 10°C.’ This is correctly labelled in child’s handwriting as ‘False’. Below this, the following true statement appears in child’s handwriting. ‘The temperature didn’t change between 1 pm and 2 pm.’ Enjoy giving children the opportunity to use situations that engage them to collect and present data in context. Be sure to check your Teacher Guide for more tips and ideas! (On screen: the following text. ‘Your Teacher guide also includes Before you teach and After the lesson reflection questions for each lesson you teach. Don’t forget to take a look!)

Question 18

How can we assess for mastery in statistics?

Answer 18

Children who have mastered this unit will recognise and read data presented in different ways. (On screen: a pictogram, a bar chart, a table and a line graph appear.) They will understand how to recognise and read continuous data represented in line graphs and will fluently draw conclusions from data sets, including compared data, explaining their reasoning.(On screen: a double line graph appears, showing continuous data for temperature against times of day on 1 December and 1 October. A question reads, ‘What is the difference in the temperature a 2 pm on 1 December and 2 pm on 1 October?’ Red lines run from the position on the x-axis representing 2 pm to the graph lines for December and October, and then to the positions on the y-axis representing 7°C and 9°C, respectively. A speech bubble appears, saying, ‘I read off the values from October and December and subtracted to find the difference.’)
Using their knowledge and understanding, they will then reason about and solve multi-step problems fluently. (On screen: a line graph appears, showing continuous data for kilometres cycled by Toshi against time. A question reads, ‘How long did it take Toshi to travel from 20 km to 70 km?’ Red lines run from the positions on the y-axis representing 20 km and 70 km to the graph line, and then to positions on the x-axis. The answer is given as follows. ‘Toshi had travelled 20 km at 10:30. Toshi had travelled 70 km at 12:00. Toshi took 1½ hours to travel from 20 km to 70 km.’

Question 19

What are the key vocabulary?

Answer 19

They will also learn the terms ‘line graph’, ‘discrete data’ and ‘continuous data’ as these concepts are introduced.
(The following text fades in and out of the screen: table, bar chart, pictogram, key, compare, altogether, more than, less than, least, most, greatest, smallest, line graph, discrete data, continuous data.)

Question 20

What is discrete data and provide an example?

Answer 20

Discrete data is a numerical type of data that includes whole, concrete numbers with specific and fixed data values determined by counting.

Examples of discrete data include the number of people in a class, test questions answered correctly, and home runs hit. Tables, or information displayed in columns and rows, and graphs, or structured diagrams that display the relationship among variables using two axes, are two ways to display discrete data.

Question 21

What is continuous data?

Answer 21

Continuous data includes complex numbers and varying data values that are measured over a specific time interval.
Continuous data are data which can take any values. Examples include time, height and weight.