Statistics Flashcards
What did discrete and continuous data include?
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.
What are the four stages of handling
data?
- Collecting
- Organising
- Representing
- Interpreting
Pictorial Ways of Representing Data
Venn diagram (not referenced in 2014 Curriculum)
- Carroll diagram (not referenced in 2014 Curriculum)
- Pictogram
- Block graph
- Bar chart / bar line
- Line graph
- Pie charts
What is a numerical representation?
Tally charts
What is data representing data?
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
What way is the x axis?
Horizontal
What way is the y axis?
Vertical
What are bar charts called?
Bar graphs
What are bar charts good for?
Are good when your data is in categories such as drama, comedy etc
When do you use an histogram?
Histograms are used in continuous data such as peoples height. Then you use histograms.
What are the differences between a bar chart and a histogram when you draw them?
You leave gaps in a bar chart not in a histogram.
What are line graph points connected together mean?
A graph with points connected by lines to show how something changes in value
As time goes by
Or as something changes
What is the best way to do collecting data – sorting data Progression steps
Birthday month 4 corners
Talk about seasonal birthday
What are the 2 variables and the 4 sub sets?
Venn Diagram
Carroll Diagram
What are the misconceptions in statistics
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
What other misconceptions can occur?
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.
How can a deeper knowledge be achieved?
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!)
How can we assess for mastery in statistics?
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.’
What are the key vocabulary?
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.)
What is discrete data and provide an example?
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.
What is continuous data?
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.
